Those chain cleaning tools sold at most outdoors stores tend to pretty useless in my experience. They run around $30, but end up being cheap and ineffective pieces of plastic. I’ve given up on them in favor of cleaning my chain manually via a method discovered on Sheldon Brown’s chain maintenance page (any man with a beard like that must be infallible).
All that’s needed is a chain tool, a bottle, some sort of degrease-ing dish soap, and water.
The process is simple. Break the chain with the chain tool and drop it into the bottle. (I use an old Gatorade bottle.) Then put in a small dollop of the soap. Fill up the bottle with water, shake it around a bit, and let it sit. The water becomes black immediately. After it has sat for about 15 minutes I’ll dump it out, rinse off the chain, and put it back into the bottle with fresh soap and water. I do this until the water stays clear, which generally takes about 3 cycles.
When it’s done, you should have a chain that’s relatively clean-ish. Dry it, toss it back on the bike, lube up, and start cruising! If the chain was really dirty, you might also want a cheap brush to scrub it down.