Combing and Brushing
I often find combs or brushes on the streets or in dumpsters. On occasions when I don't have a comb or brush, I preen my hair with my fingers in comb fashion, over and over, until it no longer looks mussy.
Shaving
I don't shave with a razor. I have a pair of scissors I found, and I cut my facial hair with them. I keep a stubbly beard, so I cut closely to the skin with scissors. If I want the more clean-shaven look, I simply cut closer to the skin with scissors. It takes a bit longer than with a razor, but it works! I experiment with various facial hair styles.
Haircutting
I used to have way long hair, never cutting it, except for trimming split ends. But as I got grey, I started cutting my own hair in a longish layered look with scissors I found. These days it varies between mostly covering the ears to below the earlobes. I layer my hair, which is surprisingly easy to do (sorry to let out secrets, beauticians!). It's basically fist-length all around the head. Just grab a clump of hair, with little finger against the scalp and snip off the hair coming out the top of your fist, level with the thumb. Be careful to not cut your thumb skin. With this as the basic, I often experiment with different lengths. If you want it shorter or spiky, you can grab three or two finger widths of hair instead. I like it shorter in the back, to avoid the mullet look. But, to trim the back, I need two mirrors: a bathroom mirror and a hand-held one. I always find little mirrors or pieces of mirror in dumpsters (dollar store ones are common). I usually wait until I'm in a bathroom (usually at a friend's) to cut the back. I haven't had anybody else cut my hair since I was maybe 20 years old.
Nails
I clip them with scissors or nail clippers I've found on the ground. If I have no clippers or scissors, I file them with sandy rocks. Biting my nails gives me the willies.