If the club was broken in anger - for example, as a result of being slammed into a tree or thrown down the fairway - it may not be replaced. If the club was broken because it was used as a walking aid, it may not be replaced. In other words, if you were doing something with it unrelated to your playing of the course, you're out of luck.
If, however, the damage occurs in the course of play - e.g., the clubhead snaps off a driver, or an iron is bent when trying to play from under a tree branch - there are options for replacement (see Rule 4-3).
The first option: Keep playing with the damaged club (not much of an option, eh?).
The second option: If it can be done without unduly delaying play, you can repair the club yourself, or try to have it repaired.
The third option: If the club is unfit for play, you can replace it in your bag with any other club, as long as play is not unduly delayed. The replacement may not be borrowed from any other player. But you can get it anywhere else - from the trunk of your car, from your locker back in the clubhouse, from the pro shop, from your Uncle Harry who always carries an extra club for you just in case.

