If you are going to be doing this regularly I recommend you look at a chain cleaner. Park Tools (
http://www.parktool.com/tools/CM_5.shtml) and Finish Line (
http://www.finishlineusa.com/Mainten...tm#Brush%20Set) both do very good ones.
You simply put a little degreaser in the bottom, fix it around the chain, then spin the cranks. The little brushs inside get your chain looking like new in seconds!
Probably only worth it if you are going to do the job regularly, but it saves me a HELL of a lot of time messing around, and my chains last a lot longer so it is economical in the long run.
As for the sprockets, spray a LITTLE degreaser on them, then run a piece of rag in between to clear out the crap. What you dont want to happen is for the degreaser to go anywhere near the bearings in the middle of the wheel, or very soon they will have no grease left in them, and then they sound like a coffee grinder!