Faucet handle has popped off, help?

If it's rented house, contact your property manager and say you went to use the tap and it broke (just tell them what happened, I trust you didn't use excessive force..). If it's your house the faucet will come apart and may just need serviced if something in the handle hasn't snapped. A picture would help. Servicing a faucet is only a DIY job if you know what your doing and have some tools. You often need a lot of force to get the tap head loose and you could do damage to the tap, sink or pipework (or yourself!) if you're not careful.

There are guides online, search for 'changing a tap washer' or 'servicing a tap' on youtube.

Pictures would help. It might not actually be broken, but I cannot say for sure. There should be some kind of cover in the center that you might have to pry up with a small, flat blade screwdriver or something of the kind, if this is the kind of faucet I'm thinking of. When you get that cover pried off, there should be a screw there that normally holds it on. The screw is either loose, or it's gotten corroded and broke. If it's truly broken off, it could be fixed by drilling out the broken part and retapping the hole, but I think that's more than you'll know how to do, or have the tools for. If it's only the screw coming loose, tighten it up, maybe use a little loctite on it, and you'll be all set.

You can buy a new faucet handle, if this trick won't work then just buy a new faucet. If you have no idea on how to change the faucet or handle it is much better to let someone knowledgeable do the work for you.

SOUNDS like someone used excessive force on the handle,too many times,and cracked it,or chipped out the inside,where it fits on a slot.Pull off a plug,located on the top of the handle,and there should be a screw,under it.Unscrew the screw,and lift off the handle,and take it to the hardware store,with you,to get a replacement handle.

if its not the previous answer, it could be a washer that needs replaced, or a new faucet.