If you pick a tattoo place that is CLEAN and well run the risk of infection is fairly low.
You want a place that uses an autoclave (and will show you if you ask about it) and one time use needles, they wear gloves and the place looks overall clean.
Doing your research on the place is the number 1 thing that will help with that.
After you have a tattoo it's important to be smart about what you're doing while you heal it. Keep it moist with lotion but clean, don't go swimming, don't soak in the tub. Wash it off then pat it dry.