I get the materials to make them like other games, but i can't seem to be able to make them. Is there a quest that has to be done before you can make arrows.
You cannot craft arrows, however...
You can farm them, either from some Imperials practicing archery in Solitude, or from Thieves Guild member Cynric Endell doing the same in the Ragged Flagon.
With Dawnguard DLC
Now with Dawnguard DLC you can actualy craft arrow from a forge with blacksmith skills. Most of the time you'll need
1x Firewood 1x Material (Iron, Dragonbone, Ebony, etc)
Example for a Daedric arrow you'll need
1x Firewoord 1x Ebony Ingot 1x Daedric Heart
So it's now possible to craft arrows if you have the right DLC installed.
You can craft arrows and bolts at a forge (Fort Dawnguard forge in the case of bolts) if you have the Dawnguard DLC. 1 firewood and 1 metal ingot (substite metal with dragon bone in the case of Dragonbone arrows) make 24 arrows or 10 bolts. It is impossible to craft arrows in Skyrim sans Dawnguard/mods.
There is no fletching skill in Skyrim; only a skill to recover more arrows, Hunter's Discipline which Recover twice as many arrows from dead bodies.
Edit: however, it seems to be added to the DawnGuard expansion
"If the Dawnguard plug-in has been installed, 1 Firewood can also be combined with a metal ingot to create 24 arrows or 10 bolts, of any craftable variety."
I took one of my housecarls, gave her one deadric arrow and took her other ones as well as her sword so she had to shoot with a bow. We went to the snow areas and hunted for anything to kill, the arrows are easier to spot in the snow. Just walking around and fast traveling to other snow areas I got 174 arrows in less that 15 minutes. When you are done give her back her fighting things and take yours
From what everyone has stated, the dawngaurd expansion gives you that ability. However, with everyone's statement about deadric arrows being shot from guards in cities or your housecarl are actually true. I have a bountiful supply of ebony arrows at only level 12, and an extensive supply of dwarf, orc, and glass. Elven arrows are a waste of time to "dupe" as they're near impossible to find on the ground.
I would suggest trying the guards method, and even go as far as "taking an arrow to the knee" in the wilds. If you haven't noticed, you occasionally find arrows in your inventory if you get shot through with some. Give a bandit that has arrows one of any arrow you want a heavy supply of, and then set him off. Best to use LIGHT armor enchanted with reduction of restoration spells and spam the living daylights out of your best healing spell, and try to stand in a corner while you take a beating...and work up that light armor skill + restoration skill in the process...hey, you could even go as far as your block skill if your feeling "adventurous".
Good luck :D