In Diablo 3 for the PC, there isn’t any type of field repairing in the game that will allow you to repair your equipment out on the battlefield, so unfortunately you’ll typically have to go back to town in order to repair your armor and weapons.
Some merchants (not all of them) have a repair tab on the right side that you can use to either repair equipped items, or all items in your inventory.
Every now and then you’ll run into a merchant in a cellar or other random spot out on the battlefield, but I wouldn’t bank on this since it’s random.
You also no longer need to repair your equipment before you sell it, since it will be repaired automatically when the buyer receives it.