Having a chain that runs smoothly can really improve bicycle performance. Wiping on grit and other matter can also make the chain last longer and also keep your chainring and cogs from wearing out. It's also something that I neglect.
Last week I took advantage of a window of time between work and a party and cleaned my chain.
I started propping my bike up on its seat and handlebars so I could have access to the chain. Then I loosed up the gunk by dabbing a bit of lubricant onto each link of my bike.
Next, I used some scraps of an ugly tshirt to wipe the chain. I did this by rotating the pedals and holding the chain in the cloth. I went through a few small pieces of fabric. I also wiped the cogs and chainring as well as my derailleur. After it was less filthy, I applied some more lube and then wiped it off again so that it wouldn't be dripping.
After that i turned the bike over again and was on my way. I had some dirt on my hands, but i washed up and was ready to party. Oh, and my bike is quieter and feels quicker. Yay!