Unenchanted items can be repaired at a variety of places, but the Fighters Guild will do it cheaper than almost anyone if you are a member. To repair a damaged or broken item, click on the smith, click on "Repair Item" select the item to be repaired from your inventory, and click on "Repair". The smith will quote you a price and tell you how long it will take. An early bug would not let you retrieve the item from the smith or else it would disappear if you left town. These bugs have been patched.
Frankly, the only items I've ever needed to repair were weapons. No matter how battered I get in a fight, my armor is always "new", my clothing is always "new" and so forth. Weapons and enchanted items are the only things needing repair.
Repairing a magic item can be a complicated process. First, you must have the latest patch (v.212 or v.213 [you don't need both]). Second, you must add the line "magicrepair 1" (no quotes and note that it is a space, not an equal sign) to your z.cfg file in the main Daggerfall directory. The z.cfg is a plain text file and can be edited with any word processor or text editor. Now that the techie stuff is out of the way, let's repair magic items.
Go to an item-maker and enchant an item, giving it the repair ability. Equip the item. Rest, rest, rest. The condition of an item appears to improve one category for each 8 hours of rest (that's an observation, not the formula).The game will select an item to be repaired. It appears to start at the top of the inventory and work its way to the bottom. The only hitch to this is that in loading a saved game the order of the items in your inventory gets reversed so top items go to the bottom and vice versa.
If you would like to avoid this little problem, there is an alternative method. Remove all magic items you DO NOT want repaired from your inventory. Don't put them on your wagon. Drop them or store them in your ship or house. They won't go anywhere. Now start resting. By dropping the stuff you don't want repaired, you force it to fix the stuff you do want fixed and you don't really have to worry about order. Keep resting until the item(s) have been repaired. Equipping multiple items with the repair function will speed up the repair process.