DONT PANIC
You need a special tool called a "chain tool" to get you chain off, unless you have a "power link" SRAM or a "connex" (Wipperman). You probably don't.
Removing the chain to clean it is nice, but not necessary. You can usually get your drive train functionally if not cosmetically clean enough with your "chain machine", biodegradable degreaser (Simple Green, Orange Cleaner), an old toothbrush or two, a little physical effort, time, and patience.
Everyone has a pet ritual. Mine is as follows:
1) After every ride, wipe the outside of the chain (rivets and sideplates) and pulleys with a rag made wet with degreaser.
2) If there seems to be alot of grit in the inside of the chain (inner plates and rollers), I will fill up my chain machine with full strength degreaser, attach it to the chain, and spin the cranks until the chain is saturated. I then go to the refrigerator and get out a beer.
3) After drinking the beer, I flush the contents of the chain machine and replace with a 50% degreaser solution and use again as in #2.
4) After waiting, without another beer since there are more steps that require finesse and eye-hand coordination, I flush the contents once more and then run the chain machine again - this time just with water.
5) Then I take off the rear wheel and use my tooth brush with full strength degreaser to scrub out the cassette and rear and front derailer. Work on the dirtiest bits first as otherwise you spread all of your gunk around. Then rinse with water and dry everything off the best you can.
6) Then put your rear wheel on again. This is the finesse part where you are happy that you resisted the impulse and had only one beer.
7) With the bike finally assembled, dry off the drive train by running the chain through a hand-held rag. Wait for an hour of two until you are pretty much sure that everything is dried off.
Finally, the eye-hand coordination part. Put the tiniest drop of lubricant (Pro-Link, Triflow, etc) on each roller of the chain. Turn the crank to get the lube into the chain's noks and crannies and wipe off the excess. Wait 24 hours for the volatile components of the lube to evaporate and ride your bike.
Other tips:
http://www.parktool.com/repair/readhowto.asp?id=24http://www.sheldonbrown.com/chains.html