Cleaning Supplies

The following are useful cleaning supplies to have on hand:

Alcohol-Some people swear by denatured alcohol, but even common rubbing alcohol (isopropyl alcohol) will work. Alcohol cuts through the clay better than soap and water, and because it dries so quickly, it doesn't lead to rust on metal tools.
Baby wipes-These wipes are popular for cleaning hands, tools, and work surfaces. However, be aware that most don't contain alcohol, so if you use them straight from the package, they won't cut through the oily residue as well as they will if you add a little alcohol. Some people caution against using baby wipes with glycerin on metal tools like the pasta machine. (See the Glass Attic link below for more information.)
Paper towels-Use paper towels dampened with alcohol to clean work surfaces and tools.
Stiff-bristled brush-For hard-to-reach or stubborn spots, try a stiff-bristled brush (dipped in alcohol, if necessary).

Hand Cleansers

Your tools and work surface are the only things clay sticks to; your hands will likely need some special attention, too:

Soap and water-Good, old-fashioned soap and water are always helpful, but with the residue left from polymer clay, they might need a little extra help.
Grease-removing hand cleaners (without pumice)-There are a number of hand cleansers on the market made especially for removing greasy dirt. Those without pumice will be easier on your hands, which is important if you're using it frequently.
Hand sanitizer-The type that contains both alcohol and glycerin can also be useful.
Hand lotions-Any type of hand lotion-even the cheapest you can find-helps keep your hands from drying out, which is a common problem when you're washing your hands frequently. Some people like to use cheap lotion to clean their hands while working with the clay, such as when switching between colors. They work in the lotion, then wipe their hands on a paper towel. You can also use hand lotion in conjunction with soap and water for a thorough cleansing when you're done with the clay.
Nail brush-This is useful if you have long fingernails. Clay tends to collect in every little crevice it finds.