Clean Bike Chain and Drivetrain
Chain maintenance is extremely important for the happiness of your bicycle, kind of like regularly changing oil in your car. As a bicycle chain is used, it stretches. As the bike chain stretches, the gears are honed out to conform to the growing length of the chain. Eventually the chain starts skipping. Not only will the chain need replacement, but so will the front and rear gears.
A clean and lubricated chain lasts longer and works better.
Clean the Chain
The simplest method to clean a chain is to hold a rag tightly on the chain and rotate the pedals to force the chain through the rag. To do a better job, apply some wet chain lube or a degreaser to the chain first, and than run it through a rag. We often spray a chain with Triflow, let it soak a minute, and then run it through a rag. The more care you take with each link the better.
Clean Chain with a Rag

Using a special brush helps.
Drive Train Brushes

A more complex and thorough process requires removing the chain. First, take the chain off the bike. Pour some degreaser in an empty, clean plastic soda bottle. Drop the chain in the bottle, cap it, and shake it like crazy. Fish the chain out, rinse it in water, and reinstall it. Lubricate the chain. Don't consider this process unless you are really in to cycling. It's a lot of trouble, requires knowing how to break and reinstall a chain, and--hey, new chains don't cost that much!
There is controversy about whether you should use degreaser on a bike chain. The most important part of a chain to lubricate is the interior, where the pins move against the inside of the links. This area is lubricated in the factory. It is very hard for a home mechanic to get lube into this area. If you use a degreaser, especially if you soak the chain in a bottle full of degreaser, the lubricant in the inside area will be removed. The result is a poorly lubricated chain that will wear faster. We never soak a chain in degreaser, and we rarely spray degreaser on a chain--only if it is really nasty.
A special kind of mess is caused by too much dry chain lube. Dry lube is basically alcohol and wax. The alcohol evaporates, the wax stays. When the wax chips off, it's time to re-lubricate. If you use too much dry lube, the wax builds up on the drivetrain. You may have to scrape it off with a knife.
Clean the Rest of the Drive Train
A dirty drive train makes for awful shifting and re-dirties a cleaned chain.
Clean the jockey wheels on the rear derailleur.
Clean the Jockey Wheel

Clean the chain rings.
Brush Off Chain Rings

Clean the cassette. It is hard to get the cassette very clean without removing it, but it is useful to do your best without removing it. Use a thin brush.
Clean Cassette
