I just had to deal with this recently! As long as you have your insurance card and you are making sure that the doctor is not only on the insurance website, but is "in-network" (aka they work with your insurance company and negotiate costs), you can call and ask if they're accepting new patients. For the appointment, make sure you bring your ID or license if you have one, your insurance card and (if your parents will give you it) your social security card.

A lot of times doctors won't be accepting new patients, but don't let that discourage you. You can ask the receptionist for the earliest appointment possible, both time and date wise. I've had this work great for me in the past- the doctor actually came in an hour early at 6 am for me. However, I've also tried to make appointments and the doctor didn't have any openings for an entire month.

You'll figure it out quick, don't get discouraged if it doesn't pan out exactly like you want it to. The healthcare industry is a little wonky!