Tattooing involves having a needle puncture your skin over and over again, so you'll need to find a way to manage that fear.
Get comfortable with the studio and your tattoo artist. Ask if you can watch someone else get a tattoo and see how they handle it. Plan on getting the tattoo somewhere where you can't see it; not being able to see it happen can make it easier. Bring a friend to have an interesting conversation with, or listen to some interesting music. Whatever you can do to make yourself relax, try it out. Good luck!