There are two main types of bats metal and wood.
Tools & Chemicals:
Cleaning rags, water, mild detergent, polish or wood oil.
Wood bats should be washed with a rag, water and mild soap then dried immediately, especially if the bat is not finished or painted. The key is to be gentle, using a soft cloth to wipe the bat clean. Aluminum bats can be cleaned the same way. For aluminum bats, try using a metal polish for an extra shine, but be sure the bat is dry first. If your wood bat is unfinished a light coat of wood oil will help protect the wood.
For ball scuffs try using a plastic pot scrubber and mild detergent to lightly scrub off the marks. Different brands of bats might be cleaned better with different products so be sure to try out different methods.