In both Fallout 3 and Fallout: New Vegas, how can I repair my weapons and armor?
You can repair your gear by opening your Pip-Boy.
Go to the item you want to repair, then press the "Repair" button it shows somewhere to the right. I'm pretty sure it's R or F on default.
If it's grayed out, and not accessable, it means your repair skill is too low, or you don't have anything to repair the item with.
You need another of the same (Or sometimes very similar) item before you can repair the original. This will discard the item you used to repair the original one with.
It's also possible to have some merchants or other NPCs to repair your items. This will cost you some bottlecaps. Some followers can also repair your items, but I believe there's a pretty big cooldown of some sort on this
You can either repair them yourself, or ask a merchant NPC to do so.
To repair them yourself, you need similar pieces of equipment ; your effectiveness at this task is governed by your Repair skill.