I think you can be 16 with your parents permission. I think it all depends on how good your artistic skills are, and the owners of the shop. They might allow you to do weekends to get you started and see how good of job you do, then allow you to work more days once you're 18. I don't think you need any special high school courses to become a tattoo artist.
You have to be 18 to legally be a tattoo artist.
As for special courses - highschools don't offer anything that specializes in such an alternative field, but taking art and drawing classes will definatly help you grow as an artist and practice.
Once your 18, bring a portfolio of your drawings, paintings, artwork, to any local shops and try and find an apprenticeship. You have to start somewhere...and the best place to learn is in a shop, watching, and actually experiencing the profession. Dont be suprised when it takes longer than you want to become a professional that people trust...a tattoo artist is a serious job and customers have to trust their artist to put ink on them that last forever.