I clean my chain anytime after I ride in wet conditions or really dusty conditions. That's what the guy at the LBS told me. Normally I'd say I clean the chain and relube it every 10 rides or so, which is about every 150 miles. I don't know if that's right or not, but it's really easy to do.

I have one of those chain cleaning devices - you put a little degreaser in the housing and add water and then snap it onto your chain and spin the pedals. You do not have to have a bike stand for this. I don't. I just prop the back wheel of the bike into a corner and spin the pedals backward (be prepared to have the chain come off until you get the hang of it). It's so much easier, and IMHO less wasteful than using a bunch of paper towels or one of those aerosol solvents. The cleaning unit definitely drips though and the black stuff that comes out will stain your concrete, so I would put a cloth towel or something like that down (or do it over your grass like I do).

As far as the rest of it goes... I just use a soft cloth dampened with water and wipe the frame clean. Then I dry with another soft cloth.