Each studio is going to be different, hopefully you’ve already checked out the place, maybe they have a TV, music, a cafe close by? What you bring is going to totally depend on how long you are going to be sitting/lying down.
First of all, make sure you have your driver's license or proof of age card with you. A studio will not tattoo you if they believe you to be underage. It is illegal, just don’t try it.
Dress appropriately and comfortably - if you are going to be getting a thigh piece that will take 6hours. . . that leather catsuit might not be the best option. Comfort is the word of the day, this isn't a high fashion show. PLEASE think of your tattoo artist, they need to be able to comfortably tattoo the area that you are getting your ink done.
If you are going to be in for a long day, bring a pillow, bring some snacks, bring a water bottle (staying hydrated is important!). It’s exciting getting a tattoo, but sitting for hours isn’t that enthralling, so bring something to entertain yourself. . . maybe not a game of twister. . . but download a movie or two on your phone, listen to some music, whatever floats your boat.