Research tattoo shops in your area. Many shops have a shop website with contact information, directions, tattoo artist bios, and examples of the artists' work.
Visit the tattoo shops you are most interested in to discuss getting a tattoo. If the tattoo artist's current state-issued tattoo license is not in clear view, ask the shop manager to see everyone's qualifications. Take note of the cleanliness of the shop. The Tattoo and Piercing Supplies website notes that an autoclave (used to sterilize items such as needles and grips), gloves, and ink cups should be present. The floors and all surfaces should be clean and sanitized at all times.
Look through the shop's example photos of other tattoos they have done. Whether you have a design in mind, or you want to collaborate with your tattoo artist, viewing the artists' portfolios will allow you to get a feel for each artist's tattoo styles and strengths.
Carefully read over the tattoo disclosure forms before signing anything. These release forms are to protect the tattoo studio and the client and will generally outline the state and shop tattoo policies. Ask questions about anything that is unclear. If you feel uncomfortable with the situation at any point, you can tell the artist you have changed your mind and leave.