My experience has mostly been playing full casters, because I love spells. I would like to play a class like the Artificer - I'm an engineer, so I love the flavor - or a Paladin, but I'm not entirely sure how to manage them. 

Full casters are some of the most powerful classes in the game, with access to potent spells and slots to cast them with. Martial characters have a sure place on the battlefield, like the Battlemaster Fighter with its peerless combat utility or the Barbarian that just won't die. The Rogue shines both in combat as a stabby sneak attack machine and out of combat as a superb infiltrator. 

But where do the Half-Casters fit? Often they seem to be stuck in the middle. I want to like them, but they feel like two halves that don't equal a whole. With a few exceptions, most of them are MAD, sacrificing either their save DCs or their to-hit bonus. They get access to spells much more slowly than full casters, making the spells feel weak for the tier of play. Their spell slot progression is likewise slowed, making each spell cast a major decision point. At the end of the day, it feels like a lot of work that results in a mediocre sword swinger with some low level spells peppered in. 

How do all of you go about playing half casters? Any tips on finding their role in the party? 

Paladins tend to use their spells for smiting a lot.  It is big on nova damage.   Their paladin only spells are mostly smite addons, that they ignore.  Main exceptions are Find Greater Steed (pegasus) and Circle of power (great defensive spell for the entire party).

They get a lot of good defensive combat abilities, including great saves, healing, immunity to fear, etc.

I have not played an artificer but they make magic items and can attune to more than 3, so I tend to think of them as mage types with permanent magical effects rather than instant spells.

I also think you need to realise that half casters have a completely different play style to full casters. They tend not to rely on their spells in combat, but rather use them supplement their abilities or give them extra utility. As such you don't really need to have a super high save DC or the like. If you try and play them like a full caster, then yeah they won't be great, but that's not how you're meant to play them.

As pointed out already, Paladins mostly use their spell slots for smiting, and they are definitely not mediocre. In the same way, Rangers use spells such as Hunter's Mark to increase damage output, or Pass with out a Trace to help with stealth.  

Artificers are again an interesting option, where they are given a lot of additional options that a regular spell caster wouldn't have, usually related to magic items. I'll also not a couple of a subclass also provide options so that your attacking stat is your casting stat as well (Armorer and Battlesmith).

In combat, a half caster will generally use a spell as an opener, for a buff, or to apply a "the next time you attack/hit a target" effect. Paladins are generally reliant on their Oath Spells for a pre-melee opener, while Rangers have a couple of field effect spells like Fog Cloud, Spike Growth, or Entangle, and can get a few more by subclass. Buffs are more the Paladin's field, naturally.  For the attacks, many of them require you to hold concentration until you hit a target which attracts some criticism due to the risk of losing the spell before it goes off; Paladins get Smite spells that trade some of the damage from a Divine Smite for additional effects, while Rangers turn ranged attacks into AoE's; generally not quite as powerful as what a fullcaster can do at the level, but a decent boost to martial damage. As has been said, these are more meant to augment martial combat, rather than being the primary element of your strategy.

For out of combat, they can do a reasonable stand-in for the corresponding full caster in early levels if there isn't one in the party, or can coordinate with them if they are in the party so the spell choices complement each other.

Purely in terms of optimized DPR, the spellcasting options aren't great (unless you count Divine Smite as spellcasting). Fortunately this isn't an MMO, so there's no need to conform to the single best damage options.

I like classifying artificers as sources of permanent magic as opposed to instant spells, that's a neat way to put it!

The other place artificers make me nervous is with their infusions being known instead of prepared. I don't mind only ever getting six infused items at a time (eight with Armorer), but being locked into your choices of infusions known makes the ability feel much less versatile. 

Artificers also have the ability to reach dizzying AC levels, but their damage is never stellar, so I don't know if they could be annoying enough to avoid the tank fallacy. 

Increasing the amount of magic items in the party does seem like a huge boon ... I think I'm just worried that a DM would count them toward the expected number of magic items a party should receive, give them less, and thus render the ability null. 

I admit Paladins don't worry me as much as the others. As mentioned by several of you, their base class features are so strong that their spells slots could all be smite slots and still produce an incredibly effective character. 

I think my main concern with half casters is resource management. I worry that having so few spell slots would be a recipe for regret, either using them all too early, or ending the day with slots left over. Even with something like Battle Ready, an Artificer making two unaugmented weapon attacks might feel less than useful in combat. 

Half casters can multi-class, taking some levels of a full caster to give them a boost of spell slots.  They can even use those extra spell slots for smiting, etc.   But it does not affect the highest level of spell they can cast.  That is, a 10th level Wizard, 10th level Artificer gets an 8th level slot, but they can only cast spells of 5th level wizard of 3rd level artificer.  Typically they upcast spells to use thee 8th level slot.

Going 50/50 is rare, more typically an artificer might take 3 levels of Wizard to get effectively +5 levels of Artificer for spellcasting purposes only. Note they get the wizards subclasses at wizard 2nd level, so most at least take two levels of wizard, if not 3.

Dipping into full caster isn't going to do much to improve a half caster's spell slot pool and really isn't worth it on its own. A small dip will get you maybe 1 more slot than being fully leveled in the class, and the more you push it, the more you delay the progression of your main class features.

Not really true. If an artificer takes a single level of wizard gives you 3 cantrips, knoweldge of 6 wizard spells of first level, the ability to learn all first level wizard spells,, Arcane recovery to regain a first level spell slot on a short rest,  and a full caster level boost to their spell casting,  Those are killer abilities at 2nd level, and reasonable gains till much later.

A second level can, if you take divination school, gives you two portents, well worth it, plus some other minor stuff.

I could see forgoing the third level.

all very cool

A lot of low level spells are still great at high levels of combat and half casters can take advantage of that.  Bless is useful at all levels but by the time the party get to level 5 the Cleric is probably wanting to concentrate on something else.  The the party have a chance to prepare of combat starts with the paladin out of range of the enemy casting bless is a big boon to the party. If someone is unconcious it only takes a HP to get them back up and all half casters have access to cure wounds (though the paldin might prefer lay on hands). Waiting for the Cleric/Druid/Bard to get them up might result in them missing a turn or even dying.  Absorb elments is just as good for the ranger as the full caster.

I agree that half casters need to watch for resource management but the same is true for full casters and also monks who have ki driving many of their features.  Some paladins will rarely cast a spell but I think it is mechanically better cast a reasonable number of spells but leave enough slots to smite on crits.

Rangers and Paladins are a bit MAD but so are monks. Mechanically a one level dip in Hexblade warlock is huge for a paladin mostly but not entirely because then can focus on charisma and only need enough strength (or dex) for their armor.  Artificers are fairly SAD, they want some Dex and con for survivability but the same is true of any full caster, once they get to level 3 pretty much all their offensive capabilities are based off Int.

Each half caster has a very different style of play and all are different from the non caster and full caster. Paladins mostly use their spell slots for smiting so they are always very melee focused. Artificers are more laid back and missile oriented in most cases. Each of the 4 subclasses has a fairly distinctive style of play and magic use. Rangers are the “true Gish” using their spells for both utility and combat. However, rangers are not really meant to tank or blast. They are experts at moving around the battlefield and controlling how others move around it. They are generalists and loners in many cases. When you multi class them with a full caster you are generally looking at wisdom casters (cleric/druid) or for fey wanderers sorceror Or a warlock dip works since they also call for high charisma. That helps lessen the MAD requirements for them. the biggest problem is that they are known casters not prepared so their selection ability is very limited. This may change with the new version coming later this year.

I try to focus on spells that enhance my ability to be a martial.  Spells that give me more attacks, or enhance my attacks are good, Spells that allow me to move or enhance my movement are great. Spells that improve my defenses are great.

I find that spells that do one shot of direct damage are generally disappointing.

Definitely avoid direct damage spells outside of cantrips, and even those are situational: an Artillerist Artificer gets good mileage out of spamming offensive cantrips, a paladin does not.  Leveled damaging spells are simply not worth it- by the time you get them they're not going to be effective enough.

Well, the leveled damage depends a bit on the context; the weapon attack riders tend to be pretty good, and even the current Conjure Barrage gets decent mileage if you've got three or more targets. Granted, it's not Cone of Cold, but even with the save 9d8 is significantly more damage than 2d8+2d6. Single target/small AoE caster spells is where you really suffer on half-casters; big AoEs can still give a good burst.

It's situational.

Granted, with 6 known spells when you can take it you'll need to make some calls on what you want to prioritize, but I've had several DMs who've run some big encounters fairly regularly, and in those campaigns I'd seriously consider it for an opener.

Yep.  I typically like to have a ranged attack cantrip for situations when I am not in melee range to hold me over until I can get into melee range...but if I had to use it, something has generally gone wrong.

Quote from crzyhawk >>

Yep.  I typically like to have a ranged attack cantrip for situations when I am not in melee range to hold me over until I can get into melee range...but if I had to use it, something has generally gone wrong.

 Pretty much.