How can I tell which size chain my bike uses? After learning how to break a chain and reattach it, and also how to add and remove a master link, I find that I can now do much more in the way of maintenance at home. I'll no longer need to bring my bikes into the shop simply for a new chain... if I can only figure out how to identify what size chain I'll need to order. 

Is there a simple way of telling what size and type of chain I'll need to order to replace the chain on a bike? Do I measure the chain links? Count links? Count gears on the cogs? 

If it helps, some of my bikes' drivetrains have internal hubs, some have derailer gears.
If you are using a bike with a derailleur the number of cogs on the rear hub will determine the chain size you will need.  They are always 3/32" chains.

You can get a 5/6/7-speed, 8-speed, 9-speed, or 10-speed chains.

If you can't find a chain that matches your cluster pick a chain for a larger number, for example if you have an eight-cog cluster you can use a eight, nine or ten-speed chain, but you shouldn't use a 6 or 7-speed chain.

Internally geared hubs will have their own specification for the size chain they require, and single-speed, fixie, BMX bikes, and probably some older bikes use 1/8" chains.