How do you 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.

No, Bethesda has decided not to do so although there is a crafting file for it in the game. Maybe they'll patch it later?

But for the moment no, just scour the world shops and buy the arrows at the stores.

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.