KEEP IT CLEAN!
Sure, this is stating the obvious -- but remember -- especially the first day or two, the tattoo is an OPEN WOUND until a skin barrier is formed again. So -- avoid things like letting your pets lick the freshly Tattooed skin (they will naturally be attracted to the smell). Don't touch your tattoo yourself if you have not washed your hands. Don't go out and lean your tattoo on a bar, tables, surfaces, theater seats, handrails, etc. -- be conscious that you are still healing.
HINT: When sleeping with your new tattoo, one way to avoid the freshly tattooed skin from "sticking" to your bed sheets is to liberally sprinkle baby powder onto them. It will not hurt your tattoo and will prevent you from sticking to the sheets like you would with a gauze bandage.