How do I fix a faucet that turns all the way around?
If the tap is working at all, it must be a cartridge type, rather than a washer (screw down) type. 

Fix #1 - It is possible that the cap nut (the big nut below the handle that the stem goes through) has risen to allow the handle to spin above the stops (which limits the minimum and maximum positions).  If that were the case, you would probably have a leak around the tap handle. If so, you should be able to screw the cap nut down, in which case the handle will re-engage the stops. You may have to giggle the handle as you wind the nut down. 

Fix #2 - The next possibility is that the stops that are broken off.  If this is the case, you may need a new piece in the faucet that incorporates the stops (if it is separate). The maunfacturer's site may offer replacement parts.  I

Fix #3 - If there is not a separate part available, and if the tap is separate (a three hole unit) you may be able to get a replacement of just the broken one from the manufacturer.

Fix #4 - If all else fails,(or if you want a fast and probably cost effective fix),  it may be worth getting a whole new faucet set.

Fix #5 - Given that you say you haven't delved into plumbing, unless fix #1 solves the problem, you probably should call a plumber.