Don't shave the tattoo until it's fully healed. If you shave around it, don't let the shaving cream or hair irritate or infect the tattoo.
Avoid using saunas and steam rooms while your tattoo is healing, as the moisture may draw pigment from the skin.
Do not cover the tattoo after the initial cover the artist applied after you had the tattoo done. Tattoos need air to heal, and plastic wrap or gauze will only suffocate the tattoo and prolong healing. When sleeping at night, simply avoid laying on the tattoo, and if you are worried about ink coming off lay a towel down underneath you to prevent the tat from becoming stuck to your bedsheets.
Avoid fluffy clothing as the fluff can get into your scabs and cause infection.