Finding a good artist can do a great job on your tattoo while putting your health at minimal risk. You will be in the chair for some time with them touching you, it's a very intimate setting and you should feel comfortable with them! Here are a few things to keep in mind while you search for your tattoo artist.
Go their shop. (If they don't work at a shop you should run the other direction!) Talk to them in person and see what kind of vibe they send you. They should be friendly, helpful and patient. In no way should they be drunk or under the influence of drugs as it impairs judgment, reaction time and steadiness, among being incredibly disrespectful. The shop should also appear clean and neat.
Use their bathroom. The way the artists keep their shop is a good reflection of their hygiene and that means how much they care about your own health. It should be spotless. Also, their own appearance should appear clean like they showered that day and do not smell like drugs or alcohol of any kind. It's worthwhile to note though that working with ink all day can dye the artist's hands and clothing, so that's normal.
Studios that stay open all hours of the night know this is the best time to target their prey, the bar crowd, try not to fall victim to that.
A good tattoo is not cheap and a cheap tattoo is not good. Most shop minimums are $50-$100, save up for your tattoo and run from shops that are cheaper than that. Cheaply run shops skimp on very important things, like sanitary conditions or good ink. You can't afford to risk it!
If the artist claims they have 10 years of experience but are only 20 years old, that should tell you that they are lying. Please ask artists their age, past work experience and overall track record. Permits can help verify age, for example our shop has all of my permits on display, even ones from past locations. This helps verify my work experience.
Health should be your primary concern. Each state law is different, but in North Carolina (NC) a permit is required and certain health standards within the permitted shop need to be kept up to par. The tattoo artists should own an autoclave to sterilize their tattoo equipment, they should be throwing away used needles in a biohazard container, they should be using gloves, they should throw away current gloves for new ones if they need to touch anything like their water bottle, they should use new needles, they should have running hot water, they should wash their hands before each customer, etc. YOU HAVE EVERY RIGHT to ask to see their current permit, testing results on their autoclave to see if their sterlization is working, etc.
Avoid tattooists who are more focused on their own vision than yours. If you want a dragon but they want to tattoo a flower, it's not working out.