You can use the Craft skill to repair an item:
Repair an Item
You can repair an item by making checks against the same DC that it took to make the item in the first place. The cost of repairing an item is one-fifth of the item’s price.
Action: Craft checks are made by the day or week (see above).
Retry? Yes, but each time you miss by 5 or more, you ruin half the raw materials and have to pay half the original raw material cost again.
What does that actually mean? There seems to be a pretty crucial piece of the puzzle missing here: namely, what actually happens based on this check?
But wait! It gets more confusing!
The broken condition itself seems to have completely different rules:
Non-magical items can be repaired [...] through the Craft skill used to create it. Generally speaking, this requires a DC 20 Craft check and 1 hour of work per point of damage to be repaired. Most craftsmen charge one-tenth the item’s total cost to repair such damage (more if the item is badly damaged or ruined).
This seems reasonably clear, but it’s totally different from what the Craft skill itself says.
Moreover, the rules for sundering seem somewhat unclear on precisely what remains of an item destroyed (reduced to 0 or fewer HP, rather than merely the less-than-half that triggers the broken condition). Is that what the Repair an Item use of the Craft skill is for? Maybe, but that doesn’t actually seem to be stated anywhere. In fact, so far as I can tell, the rules seem to imply that a destroyed item simply no longer exists, has nothing left, not even dust. As one friend put it, the item has “entered the rules hole.”
I feel pretty comfortable reading and interpreting Pathfinder’s rules, but I’m seriously at a loss with this. Is anyone aware of any rules I’ve missed, or any clarification, errata, or developer explanation? For reference, I really need to know what the rules themselves actually are, or failing that, a real consensus among the Pathfinder community, because this is for a third-party product that needs to be compatible with Pathfinder. Hard to do that when I don’t even know how Pathfinder is supposed to work in this regard. As such, personal experience or preference is not useful to me, and cannot make an acceptable answer to this question, unless you can demonstrate that your approach is a widely-used one or something.