Here are some of my tips, based on nothing but my own experience.
1) Do not drink 24 hours before getting tattooed. I once got told off by my tattooist for drinking one single vodka the night before. She said she could tell I'd had a drink, as it makes your blood thinner, and therefore you bleed more while being tattooed. You're paying for a piece of art that will last for life, don't make it harder for them to get it right.
2) Wear clothes that suit the area you're getting tattooed. If you're getting your thigh done, wear a skirt (if you're a skirt wearer!). If you're getting your shoulder done, wear a vest. Many shops have open tattoo shops, where the general public can see you getting tattooed, so you will feel more comfortable if you don't have to take your clothes off.
3) Sit still. You want your tattoos to have straight lines don't you? Particularly when your artist is doing the outlines of your tattoo. Save your chatting until the outlines have been done. Some artists like to talk more than others. Try and judge it before you start telling your life story. You want the best work they can produce and if they need silence to produce that, give it to them.
4) Eat before the appointment. It would be embarrassing to faint wouldn't it? When your body is getting tattooed, it thinks it is being hurt, and therefore starts pumping adrenaline ready for fight or flight. Some people get addicted to this adrenaline rush, I however just get exhausted after. If you have low blood sugar while getting tattooed this can cause all the adrenaline to make you feel weak, and can cause fainting. Make sure you have eaten something substantial at least 4 hours before. I always eat afterwards too.
5) Make sure you're clean. Your tattooist will be up and personal for a few hours, they won't appreciate any icky smells. You will sweat while being tattooed, so make sure it will be clean!