Aside from removing mud and grime there isn't much cleaning to be done on a bow. Since there is no explosion or burning going on there isn't much residue involved which would require such maintenance.

The string does need to be waxed periodically, nothing too intense- just smudge it on and then rub it in with your fingers. I believe the latest is the silicone wax. Whatever you use get some that is designated for bow string (not just candle wax ).

Arrows? water and a rag? Maybe some earth scented anti-microbial soap if you want to get them scent free.

BTW, before each hunting season my entire rigs will get a rub down with earth scent eliminator spray on a paper towel, arrows to. After that about once each week/weekend hunt. Keep an eye out for any paint removal- I've read where some will remove paint, but can't say I've seen it yet.

Remember to remove your wrist sling and wash it (hand wash in earth scent anti-bacterial soap & air dry). Do the same with your release.