So I’m still a fairly new at running a game. So my party found and island with an iron mine. They rescued the natives, and have now set up this as there home base. However I don’t know how much iron would be produced in a say a week. Also should I add more to the mine like gems or even other material?

After a bit of research and calculations, the average independent corporate mine produces 6 to 5 thousand pounds of iron per week. There is a lot of assuming I'm doing here to make a mechanic: they probably don't have a major corporate structure, and it propably isn't a major mine. I'd roll 2d4 for every week that the mine is focused on and have the following happen:

2: The Mine produces mostly dross. They extract 1d6*5 Pounds of usable Iron Ore.

3: The Mine produces a below average amount of Ore. They extract 3d6*5 Pounds of usable ore.

4-6: The Mine produces an average amount of Ore and a few Semi-Precious Stones. They extract 5d6*5 Pounds of usable Iron Ore and 1d4 gems of 50gp or less.

7: The Mine produces a good amount of Ore and some Semi-Precious Stones. They extract 7d6*5 Pounds of usable Iron Ore and 2d4 gems of 50gp or less.

8: The Mine strikes Precious Stones. They extract 2d4 gems of 500gp or less.

above rolls seem ok. If you want to mix it up, you can add a d20 roll to see if something highly random occurs, e.g.
1 - the mine digs unnaturally close to and awakens a terrifying monster (see Mines of Moria in LotR)
2 - the natives go on strike demanding better pay and conditions (especially if you roll a bunch of bad rolls that turn up "random monster attacks" or "mine accident occurs")
3-5 - various forms of random encounter or mine accident
6-16 - nothing noteworthy
17-19 various forms of good luck, including, natives figure out mineralogy/engineering to increase efficiency, giving permanent +X on output
20 - the miners strike a vein of:
(have a 2nd list, say, ranging from gold and platinum to some sort of Unobtainium)

Have your players expressed an interest in becoming iron moguls?  Do you want to upend your current campaign plans so that they can invent the blast furnace, smelt ore into ingots, build a shipyard, form trade alliances, negotiate with their workforce, and become rich ******bags who put their names on libraries, rather than guys who get in sword fights with monsters?  Would they, in short, prefer to be playing a resource management board game?

If not, who cares how many tons of ore they can extract?  Just give them 100gp/week.  And yes, you should absolutely add more stuff.  The whole thing should be full of gems like in Snow White, and monsters like Moria, and then the Drow should show up from underneath and drag them into a war against the Mind Flayers.  They should have a misunderstanding with an earth elemental and build a golem factory.  

It should either be completely tangential to your actual story or totally awesome, is my advice.

This is cool. I can think of several spells that could speed the digging of a mine and the location of resources.

Also, If I were DMing, there would be a 100% chance of the miners delving too deep and awakening something. Maybe after they take care of that something, there would be a new area to explore and more valuable resources to mine. 

The party now wants to make a shipyard and our artificer plans on making golems in his build a bear workshop. All his constructs look like bears. We have a magic crafter looking to make magic items. The dwarves in the party (we have three) even sent word to their clans to send aid. So I'm expected to bring other craftsman.

Wow.  Well, I guess that's your campaign now.  

Well, they can fight pirates trying to steal their shipments, they can engineer wars between countries to drum up business for their iron.  They can invent railroads and build new empires.  The new dwarven craftsmen could clash with the indigenous workers.  Lots of dramatic stories there.  Could be fun, if you want to go all in on that.

If you had any other plans, I guess a volcano could erupt, killing all their clansmen and sealing the mine forever.  Or you could just say there was SOME iron in the mine, but now it's played out.  What was the campaign supposed to be about?  How badly does this throw things out of whack?  If they end up selling weapons to the guy they were supposed to stop from taking over the world, is that going to upset you?

If you are good with the direction it’s going, then go for it. You can basically treat it like any other base or castle, with raiders coming to steal their stuff. If it’s profitable enough, it would likely attract the attention of some other power centers in your world, like a baron, church or cult which wants to control it, letting the players decide which group to ally with and which enemies that will create.

If you’re not into it, have an out of character discussion with them about how the game is not called Payrolls & Spreadsheets and do they really want to role play being small business owners vs. Heroes fighting monsters and saving the world.  Get everyone on the same page about what kind of campaign you all want to play and then go ahead and play that.

I’ve had to change the original campaign but they want to fight pirates, then they will get pirates. I have an old PC I plan on using The pixie Pirate Captain Hawthorn. He’s gained a legendary magic artifact and with his fleet he now plans to take control of an archipelago. Now the party needs to build a more combat capable flag ship and gain ally ships or build more. 

How large should I make Hawthorn’s fleet officially (from his previous adventures) he has two warships, but how many should i add to make a fleet. This fleet is supposed to come in at the final battle. The party are at least an 8 month journey from Hawthorn.

How about 2 Warships, 4 Galleys, and 8 Keelboats? Keep the official amount of Warships, increase the armada to a total of 14 ships.

Not that running a mine is out of the question, but mining is very labour intensive and often dangerous.  Poison gas, lack of oxygen, cave-ins are some of the common dangers of mining.  A profitable operation would also require more than a few people at work.  If you have NPCs doing the work for them, how are they planning on paying these workers?  If they are on an island, they would also need to arrange for regular shipments of food and probably also some entertainment to keep the NPCs from going crazy.  

Payment has not been established yet, entertainment is not a problem, we have our bard that tactually acquired a war ship that he now has turned into a party boat, the cannons now fire confetti.  

Well, don't get caught up in making this more realistic than it needs to be (though that doesn't sound like a problem so far).  I mean both in terms of running a business AND running large-scale naval battles.  I'm glad you've got a villain and you're pointing your story to a final confrontation with the pirate fairy, but you said you were new to DMing, and both resource management games AND naval wargaming take some practice.  Be careful to stay in your comfort zone.  Feel free to gloss over whatever details you need to to keep things moving.

My point is that a resource management game on top of the regular DM job that the OP is doing seems kinda much.  Unless Xander is into some serious note-taking and logistics charting.  The stuff I listed is mostly to shake up the PCs so that they either get more exciting stuff to do at their place of business or to discourage them from turning it into a Sim Mine game.

My plan is for the party to use the mine as a home base and navel yard to construct ships but be sailing around either destroying the enemy ships one at a time or even capturing them. As there gone ill be rolling on a chart i made up thanks to help from Slade Tracey and JCAUDM. The team leader is good at managing the party and his growing fleet and his 2nd is experienced in managing resources. So I think we got this, plus the group has to take a couple weeks off till we are all back in the states together. So ill have time to prepare more. 

well depending how they set it up it can be one hell of a fort so long as there careful with cave ins or having fresh air in the deeper parts of the mine and if they need more room well there that pick axe or a spell that molds earth and rock.

Gotta say, I love it! There's so much you can do from here, from establishing a situation where multiple nations' claim the island as a part of their territory (faction intrigue, could lead to them becoming privateers or an assassination mission) to Mines of Moria and Underdark situations to simply a humanitarian aid situation where they help the native population maximise their use of the island's resources and set them up as a target for marauding pirates. I agree with an above poster that it should either be totally tangetial or absolutely awesome (I'm inclined to go with the latter). As for playing Payrolls and Spreadsheets, hey, your campaign, do your thing. I love building an economy into my worlds (most recently, I offered a player an investment opportunity into fruit trees and had another player who wanted to buy a kitten deal with a pushy, upselling retail assistant) but it can get burdensome if you're not into that. It can definitely be considered worldbuilding though! :)  

I feel like you could put a loot table depending on the situation if you want to use this somewhere else like for example, one of my characters has a mine in the star metal hills near neverwinter in the forgotten realms mainly in the dragon of icepire peak campaign and could have some different loot tables like for higher rolls, more explicit rules on more precious metals like gold or mithril.

For use anywhere else, I would calculate in GP as to make it a bit better. This is what I have and I would like help filling it out just to make it more like a real loot table.

roll 1d10 per workweek (8h/day) per team of at least 20, else divide roll by 2 rounds down.
Depending on area,
Scarcity of materials: -2
Lacking materials: -1
Plentiful materials: +1
Abundant materials: +2

-1-3: resource table 1
4-7: resource table 2
8-11: resource table 3
12: resource table 4

Resource table 1
-1-1:
2-3:
4-5:
6-7:
8-9:
10-11:
12: roll on resource table 2
Resource table 2
-1-1: roll on resource table 1
2-3:
4-5:
6-7:
8-9:
10-11:
12: roll on resource table 3
Resource table 3
-1-1: roll on resource table 2
2-3:
4-5:
6-7:
8-9:
10-11:
12: roll on resource table 4
Resource table 4
-1-1:
2-3:
4-5:
6-7:
8-9:
10-11:
12:

First of all, this thread is five years old so the campaign is likely done by now and second of all, no.  Don't make some sort of big complicated chart for operating a business in D&D.  If you really want to actually do the running of a mine, livery stables, or whatever other random business the PCs might come into ownership of, there are better games already available for that.  For D&D purposes, a business should simply generate some regular monthly income and provide the occasional plot hook.