Chains wear out pretty fast, especially if they're dry or dirty. Worn chains cause cogs to wear much faster, in turn. Change your chain regularly before it's too worn and you can keep your cogs longer!

The briefest primer I can come up with:

• Multi-speed freewheels have many cogs in a block which threads onto the hub. The ratcheting mechanism that goes click-click-click when you stop pedaling is in that block.
• Cassettes have many cogs which slide onto a carrier on the hub, then lock into place with a threaded lockring. The ratcheting mechanism is in the hub.
• Single-speed freewheels have the same threading and ratcheting mechanism as the multi-speed. Make sure you install it with the tool notches on the outside or you're going to have a bad time when it's time to replace it!
• Fixed-gear track cogs thread onto the hub, and are held tight with a reverse-threaded lockring.

If you're indexing your shifting (with a click every speed) you need to match the number of cogs to the number of discrete positions on your shifter. If you're friction shifting, go wild.

You usually get what you pay for in durability and reliability in this section, but the big huge cassettes sometimes have a price premium for lighter materials.