I am an artificer in a campaign i am playing, I want to build the slippers of spider climbing. If I were to find something in my campaign that could help me build this would I be able to do that? 

I believe there are rules for players making magic items in Xanathar's Guide, and after 10th level, Artificers can do it faster for Common and Uncommon items than other characters.

At 10th level, it is also one of the items from the replicate magic item infusion. 

Here's a quick summary of the contradictory rules for making slippers of spider climbing, and I will make houserule recommendations in-place.  Rules are on DMG p128/129 and Xanathar's p129.

• Prerequisites on the crafter to craft the item (you can combine roles, with different PCs meeting different requirements):
  1. Both books state you must know the formula. 
     • For ease of book-keeping, I recommend ruling that an Artificer knows the formula for any infusion they could know right now, so a 10th level Artificer knows the formula for Slippers of Spider Climbing.
     • Other than that, lock formulae like you do wizard spells, so they're findable treasure.  Common recipes should generally be Common rarity, and no item's recipe should be more common than the item itself, but you can either lock recipe rarity to item rarity for a high magic campaign, make it 1 step rarer for normal magic, and 2 steps rarer for low magic (anything rarer than Legendary doesn't exist - the recipe is lost and the item can't be made).  Recipes can be taught, one at a time, using the training rules in Xanathar's - each recipe works like its own tool proficiency.  A recipe object works like a teacher that can only teach one student.  However, only let students learn recipes if they have spellcasting, an appropriate lore skill proficiency for the spellcasting (see below), and an appropriate tool proficiency already.  A higher proficiency bonus is needed to learn recipes for rarer items: Common/Uncommon/Rare/Very Rare/Legendary = 2/3/4/5/6.
  2. The DMG states you must be a spellcaster with spell slots and be of a character level defined by the rarity of the item (level 3 for Uncommon, which is the Slippers), and for an item that produces spells, you must cast that spell once per workday (this does not apply to Slippers of Spider Climbing).  Xanathar's states you need at least one of the relevant tool proficiency (presumably cobbler's tools for slippers) or Arcana.
     • To fix the DMG, replace the level requirement with a better slot requirement: making a magic item that doesn't produce spells requires you to spend spell energy, in the form of a spell slot, once per workday.  You need a higher level spell slot to make a rarer item: Common takes 1, Uncommon takes 3, Rare takes 5, Very Rare takes 8, Legendary takes 9.  You can spend a higher level spell slot than needed (so Warlocks aren't banned from making lower tier items).  If you can cast a spell without consuming the slot, the GM agrees the spell is appropriate to the item, and the spell is of the necessary minimum spell level, that suffices.  For example, if you could 1/long rest cast the Spider Climb spell as if from a third level spell slot, that would suffice for magic item creation.  This means an Artificer typically needs to be level 9 to make Uncommon magic items, but can do it as early as level 2 if a level 5 full caster is on hand to provide spell energy.    The reason for these spell levels is to match spell scrolls.  Here's a full spread of that:
       1. Common: Artificer 2/Wizard 1, and the Artificer knows every formula at once.
       2. Uncommon: Artificer 9/Wizard 5, but the Artificer knows some formulae at level 2 and more at 6 and 10.
       3. Rare:  Artificer 17/Wizard 9, but the Artificer knows some formulae at level 14.
       4. Very Rare:  Wizard 15
       5. Legendary:  Wizard 17
     • To fix Xanathar's, require proficiency in both the tool and a relevant lore skill which varies by slot (this may require GM intervention for abilities that let you produce spells without any guidance, like Barbarian spellcasting): Paladins and Clerics use Religion; Rangers and Druids use Nature; Wizards and Artificers use Arcana, Bards can use any of the three.  Warlocks choose one of the three during character creation, depending on their relationship to their patron: Religion is appropriate for a cult, for example, but Arcana is appropriate for someone conducting a ritual to sell their soul for power, and Nature can be appropriate for a patron like the Fathomless or the Genie or the Archfey, if you went too deep into wild places.  Sorcerers use History, as what they need is knowledge of their own family tree.  Other classes and subclasses need to be assigned appropriately - Eldritch Knights and Arcane Tricksters would use Arcana, since they're fake wizards, but Totem Warriors would use Nature and Ancestral Guardians would use History.  Read the fluff text for the class or subclass and assign an appropriate Lore skill.  Multiclassers need all constituent skills to use their combined slots - so a sorcadin needs religion and history.
       • Alternatively, an Artificer with an infusion of the item in existence can draw energy from it for this purpose, counting the infusion as 1 spell slot every 8 hours.
     • Now I recommend combining the two as follows: a full craftsperson knows the recipe and has proficiency in the appropriate tool, the appropriate lore skill for the spell energy being supplied, and can supply the spell energy.  I'll cover working together as a team below.
• GP cost of raw materials to make the item:  both books have escalating costs by rarity which do not match each other. 
  • The DMG contradicts the PHB - it states that potions of healing cost 100 gp to make, which even if halved means they're sold at no profit, and the DMG does not say to halve costs for consumables.  I accordingly recommend the Xanathar's rules for gp costs, base, but allowing the crafter to choose the DMG costs if they want, to work faster - I'll explain below.  It only matters for Common items.
    • However, Xanathar's costs have their own problems, because they don't tell you to also make the base item - for slippers of spider climbing, you don't actually have to make the slippers.  Where this becomes deeply problematic is when the base item is expensive, like magic plate, which per Xanathar's costs less to make than mundane plate.  The fix is easy: make the crafter also make the base item, so for magic plate, you'd need another 750 gp of materials and the appropriate time spent.
    • Alternatively, you can use the Xanathar's rules for consumables and the DMG rules for static items, which will make all static items cost more money and more time - depends on how rare you want magic items to be.
• Time cost to make the item: The DMG says a crafter can turn materials, measured in their gp cost, into an item at 25 gp per day, and Xanathar's gets weirder: it says mundane and common items can be made slower, at 10 gp per day, and magic items have you consult a table by rarity - uncommons are 20 gp per day, rare 40, very rare 160, and legendary 400.  Note that at no rarity does this speed match the DMG.  Both books have nonzero rules for collaboration: adding workers to a job to cut the time needed to time/workers, essentially.
  
  • For Common items specifically, this means the DMG rules are faster than Xanathar's: the DMG lists 100 gp and 4 days, while Xanathar's lists 50 gp and 5 days.  I recommend letting crafters choose to make a rush job with pricier materials if they want, so let the crafter choose which gp and time cost to use.
  • Otherwise, Xanathar's is always less time and less money.  As I mentioned above, I recommend picking between the two based on how rare your DM wants items to be in the campaign.
  • Xanathar's has rules for collaborating on a mundane item, but has separate rules for magic items which fail to cover collaboration.  Collaboration isn't banned, the rules are absent.  For a mundane item, provided every contributor has the tool proficiency and their own tools, subject to GM discretion for saying it's impossible to have that many people work on something that small at once, every contributor contributes the same speed (10/day).
  • The DMG has collaboration rules gated only by level - anyone of sufficient level for the item's rarity can contribute as a full crafter (25 gp per day), provided someone actually qualified is doing the actual crafting and they're assisting.
    • I recommend using the Xanathar's rules for time cost by rarity, but adding collaboration rules as follows.
    • Spell slot energy scales with both provider level and number of providers, but let  proficiency-havers provide a work team of up to their proficiency level with their proficiency, but they count as a member - so at proficiency bonus 3, a team with 1 recipe-knower, 1 lore-knower (assuming all three use the same lore), and 1 tool-knower can function as a craftsperson, assuming they have the spell energy.  At 4, you could have a fourth person be the spell energy source.  If you can make a team that satisfies the requirements an integer number of times, that's how many workers it counts as for crafting speed (see below) - e.g. if a team has 2 recipe-knowers, 2 tool-knowers, 2 appropriate spell slots, and the appropriate lore skill for each slot, it's 2 workers, and works twice as fast.  Every tool-knower needs their own toolkit, but in general they can share an appropriate workspace of appropriate size, such as sharing a forge.
• The DMG explicitly states that by GM fiat you can declare an item needs something arbitrary on hand, like alchemist's supplies or lava.  Xanathar's specifies that for mundane items, you need, on top of tool proficiency, the actual tool, as well as whatever other equipment you need (like a forge for blacksmithing), and then forgets to include those rules for magic items.  Xanathar's also says to gate a particularly rare component behind a creature of rarity-dependent CR (within a range for each rarity), explicitly stating that this can be a body part, a guarded location, whatever.
  • The fix for tools and such is easy - treat magic items like magic mundane items, just like the fix for the gp cost of making magic plate.  So crafting magic plate requires smith's tools (see the collaboration suggestion above) and a forge.
  • The lava thing isn't a real rule, since DMs can always do anything by fiat.  Any DM can houserule whatever they like.  Accordingly, of course you should feel free to do this.
  • The Xanathar's guidance for facing a monster is nearly impossible to follow without introducing weird problems, like accidentally making it trivial to farm something you intended to take real work to get, and other potential issues abound.  Plus, you have a finite stable of pre-existing monsters, and it's exhausting coming up with a new monster for every item.  Plus, stat blocks often leave out information you need to intelligently pick something - e.g. spiders don't have actual rules for making webbing or anything, you just have to know they do.   Usually, I recommend hand-waving this away - let the party do downtime things during downtime, and then get back to adventuring.  Only do this for items important enough to warrant the time and energy of coming up with an in-depth explanation of what you need to make this item and why it's not readily available.
• The DMG makes the modest lifestyle free and the comfortable lifestyle cost half (1gp/day) while working on a magic item, without explanation, but I think the explanation is that modest lifestyle is the bare minimum to rent a workspace, and the crafting costs assume this.  Xanathar's makes no mention of it.
  • I recommend copying the rule - 1gp a day minimum spent on your lifestyle ensures you have a workspace - but throw away the rule that you get a discount on this for crafting.  Just charge rent.

So here's my suggested homebrew solution to the self-contradictory and often absent magic item creation rules for an artificer making permanent, real slippers of spider climbing on their own, without help:

• You will need the recipe, which you get automatically at level 10.  You can learn it as early as level 5 if you find the recipe as loot (or buy it, by GM fiat) or hire someone who knows it to teach it to you.
• You will need proficiency in cobbler's tools, an actual set of cobbler's tools, and a workspace where you can work undisturbed.  Rent on the workspace will cost at least 1 gp every 24 hours, and no-one rents for less than a week at a time unless they're an inn, which doesn't come with a workspace - ask your GM if you can rent a workspace on a daily basis.
• You will need proficiency in the Arcana skill.
• If you're using Xanathar's time and money:
  • You will need 200gp in raw materials for the magic, and half the cost of slippers in raw materials for the base item, but this will likely be negligible - ask your GM.  Common clothes are 5 silver for the entire outfit, and while the most expensive part of any practical set of clothes is the shoes, obviously this shouldn't cost you more than 25 copper and probably less.  Assuming you rented modest accommodations for a week, that's another 7 gp, so your total cash needed here is $207.25.
  • You will need to spend 80 work hours on the enchantment and an amount of time on the base slippers based on the gp cost of the slippers, but assuming 25 copper for the raw materials, 12 minutes.  That's doable in 5 days and change if you're determined, 4 days and change if you're a determined elf.
• If you're using DMG time and money:
  • You will need 500gp in raw materials for the magic, and otherwise Xanathar's costs, so $514.25 (assuming two weeks of rent).
  • You'll need no more than 160 hours and 12 minutes of worktime, which is 10 days and change with determination, 8 days and change for an elf.  Either way, you probably need to pay 2 weeks rent.
• You will need either a level 3 spell slot for every 8 hours of work you're going to do, which you'll have by level 9 unless you want to work more than 16 hours a day (if you're an elf, you might - you can afford all 3 slots at level 11), or you need a slippers of spider climbing infusion on hand to work with.
• Ask your DM if they want to require a special resource, locale, etc to make the slippers, or if you can just make it. 

Bear in mind rent, above, is for a lifestyle, so it covers food, lodgings, etc on top of the workspace.  To help your DM decide how rare slippers of spider climb should be, Xanathar's makes them about as hard to get as a breastplate, aside from the potential CR challenge.  The DMG makes it about as hard to get as a spyglass, aside from fiat requirements.