Talk to any tattooed friends you may have about the artists they go to. This is the single best way to get a good idea of a tattoo artist's reputation and skill level. If you see work on someone that you think is high quality, don't be afraid to ask the person where they got their tattoo--even if it's not someone you know particularly well. Most people who are happy with their tattoos are not shy about talking shop about body art.
Visit the shop. You will need to see firsthand the condition of the surroundings to have a truly good idea of what kind of artist you are booking. Browse portfolios at the shop to get a broader view of the artist's work and observe things like cleanliness, attention to detail, organization, etc. Sanitation is a huge part of a reputable shop's upkeep and any reputable artist will be sure to work at a clean, sanitary tattoo parlor.
Present your design. Discuss your idea with the artist you have in mind or show them the design you already have and gauge feedback. A reputable artist will take no issue with doing custom work for you and talking with him or her will give you an idea of their level of professionalism.
Ask for a cost estimate. Don't be afraid to pay a lot of money for a good tattoo. Any artist willing to cut you a deal means they are either an apprentice (student) or do not take pride in their work. With permanent body art, it is always worth paying full price for a job well done.
Remember to tip. Tattooists provide a service as well as a custom artwork. Tipping etiquette as the same as for a restaurant. Tip at least 15 percent, especially if you plan on being a repeat customer.