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How a Fixed-Wheel Bike works
Fixed Wheel hubs have two threads on them. The larger of the two threads takes the track sprocket, the smaller reversed-thread uses a special lockring. The way this works is the lockring screws in backwards and if the sprocket tries to unscrew, the lockring tightens. This is important because to slow down on a fixed wheel bike, you push back on the pedals which would otherwise stop the bike from moving.

New Wheel or Old Wheel
For the lowest cost option to building a fixed gear bike, you can use your old rear wheel, and just replace the hub. The faster way to get your fixie rolling is to buy a new fixed-gear wheelset. The biggest advantage of a new wheelset is that you can run a lockring to hold the rear sprocket on.

Spacing
The spacing of a bike is the distance between the two rear fork ends. It is measured in millimeters and when buying fixed gear hubs it is important to know what the spacing of your bike is. The best way to measure the spacing of your wheels is to use a ruler to get the distance between the inside edge of the two locknuts.

Usually a road bike will have a spacing between 120 mm and 130, track bikes between 110 and 120 and mountain bikes are usually 135 mm. It is best to either measure it yourself or look at the bike's documentation.