You'll want to shift them a lot while you're cleaning them. The old grease gets pretty hard and you'll want to move the parts as much as possible to get the solvent/degreaser to break it up.

You asked what pawls were in an earlier post. Think of them as small claws that grab the teeth on a cog as you push the lever. They have small springs that allow them to slide over the teeth in one direction but grab in the other. The grease that's used to lubricate this mechanism gets hard as it ages and doesn't allow the claw to move like it should. You basically want to melt this old grease away to allow the parts to move freely again.

This will give you a look inside a shifter and some basic tips.
http://bicycletutor.com/rapid-fire-shifters/

On a tangent, I wonder if using some moderate heat would help speed up the process? I may get a cheap hair dryer for my bench and give that a shot next time I get some frozen shifters. Seem to get at least 1 every 10 days or so.