Yes, you need to buy a freewheel. It's almost certainly a standard one so you can go into any LBS and grab whatever they have.
The main thing to know is that it should screw on easily by hand. If it doesn't you've either not got the thread started properly, or the thread is the wrong size. Ideally put a tiny bit of grease on it so it'll come off more easily when it wears out. Chain lube is better than nothing if you don't have grease.
This is one of those things where it's a trivial task that takes less than a minute, but if you stuff it up you have to live without a freewheel or buy a new hub, which usually means a new wheel. So it might be worth paying a bike shop to do it (they should do it on the spot if you bring in the wheel rather than the whole bike, since it's quick and easy).
Getting it off is where you need a special tool. The ratchet mechanism means that putting it on the wheel is the non-rotating direction, but getting it off means having a tool that locks on to the central, non-ratcheting part of the freewheel.