Conventional Freewheel-type Hubs

The cheapest way to convert a multi-speed bicycle into a fixed gear is to use the original rear hub, assuming that it is made for a conventional threaded freewheel. A fixed sprocket will thread right on, but there is no provision for a left threaded lock ring.

If you go this route, it is a good idea to use LocTite or a similar thread adhesive. You can use an old lock ring from a British-threaded bottom bracket as an additional safety measure, it is the same thread.

Although you can just screw on the sprocket and put everything together, the chain line will probably be incorrect. If you go this route, you will usually need to re-arrange spacers on the axle to correct the chain line, then re-dish the wheel so that everything will track correctly.

I should mention that there are those who say you shouldn't use a lockring. This theory is based on the fact that if the chain should come off the chainwheel and get caught, a sprocket without a lockring will just unscrew, rather than locking up the rear wheel.

My feeling is that it is better to use a lockring so that you can rely on being able to slow the bike down with your feet, especially if you ride with only one brake.
If you don't use a proper track hub with a lockring, you really should have two hand brakes. If not, a front brake failure followed by a sudden extra effort at "resisting" could break the sprocket loose at the worst possible time, and you'd be toast!