There's a lot that needs to be clarified here.

First, there are cogs for multi-speed bikes as well as track cogs. If you want to convert to single-speed, the first thing you need to do is determine what type of hub you have. Sheldon Brown has a photo to help.

If you have a cassette hub (also known as a freehub), multi-speed cogs have splines on the interior that slide onto the freehub. Removing the unnecessary cogs from your cassette hub and installing spacers for a correct chainline will get you a single-speed setup. If you have a freewheel hub, the entire freewheel assembly threads onto the hub interface. You can remove the entire multi-speed freewheel and thread on a BMX freewheel. If you go this route, you will also need to rearrange the spacers on your wheel's axle and re-dish the wheel to center the rim in the dropouts.

If you're looking to go fixed, you would use a track cog and lockring on an appropriate hub. Typically, track hubs are of a "flip-flop" style, which has freewheel threads on the opposite side. Purchasing a track wheelset is usually the easiest way to convert an older road bike, because you'll spend less time fiddling with spacers and you won't need to re-dish the wheel.