Just like anything, you can put as much effort into this as you want. If your a casual rider, toothbrushes and simple green will do you just fine. If you find yourself riding several times a week, then you will probably want to clean your chain more frequently, so I would suggest one of the snap on chain cleaners like the park mentioned above. They work very well and make the process a lot faster and easier.
After cleaning, I would rinse with water, if you have an air compressor, blow the links out and dry to remove any last sludge build up. Then lube up. If your climate is dry, I reccomend "dry" teflon lubes. Which leave less of an oily/greasy build up for dust to stick to and accumulate.
My process for lubing... spin the chain backwards so it free wheels and apply lube generously as it goes around. Once you've lubed all the way around, spin the crank a dozen more times or so backwards to work the oil in. Then grab a shop rag and grab around the chain, continue to turn the crank backwards and soak a bunch of that oil off. Turn the rag around regularly until the oil stain gets smaller, you don't have to do this until there is no stain, you just want to get most of the extra lube off. Extra lube will just cause grit and dust to accumulate faster, don't worry, you can't wipe too much away, it will stay in the moving parts where it is needed.
After each ride, repeat the oiling procedure above, you should then only have to clean your chain every month or so. Depending on the conditions you ride in of course.
As far as the rest of the drivetrain, If you have the time and motivation, I would dissasembly the idlers on the chain tensioner and clean them off real well, depending on the quality of your componenets the idlers will have sealed bearings or bushings, in the case of bushings i usually slap some grease in there and re-assemble. Same deal, wipe away any extra grease to keep it from attracting dirt.
Don't forget to spray some of that lube in the shift and brake cables anywhere that the cable comes out. Spray in then work the lever or shifter a few times, this will help extend the life of your cables and housings.
I can give lube advice all day, if you want more just let me know.
Ed