From a medical point of view, you can get a tattoo even if you’re 5 years old, except that your body would have to grow significantly, and as it is growing – the tattoo will be damaged. If you are, lets say 13, you are still going to grow, but not in such a significant way. The changes in the tattoo will not be obvious, unless you got a very symmetric or precise tattoo.

By the Israeli law you are allowed to get a tattoo (and the tattoo artist is allowed to give you one) at the minimum age of 16. In the rest of the world the rules vary, and there are countries in which you are not allowed to get a tattoo before the age of 21. You might want to carry an ID when coming to the studio so that you can prove your age, incase you look too young. If you are not yet 16, your parents will have to approve, and will have to supply you with a written approval and include their phone numbers, incase their approval has to be verified. Some artists would simply ask that your mom or dad will join you to the studio.
Most artists would simply prefer to avoid the bother, and refuse to tattoo you if you’re under 16.
Most artists would refuse to tattoo private parts, as well as very visible parts of the body (such as neck, forearm etc…) if you’re under 18.
Check that upfront with the artist.
Don’t try to fake an approval or let the tattoo artist speak with some cousin of yours over the phone. The tattoo artist isn’t stupid and you’re just gonna make fools of yourselves.

Whatever you do, don’t try looking for a tattoo artist that doesn’t require or demand approvals! Such a tattoo artist that does not obey one law – certainly doesn’t obey other laws such as professionalism and sterility. Most parents would rather succumb to your request and approve your tattoo, than taking the risk of you going to such a tattoo artist.
Just reason with them, promise to give good grades at the end of the school semester, and in the end they’ll agree. And if not, worst case scenario, wait a little while longer…