Drawing and doing tattoos are two totally different things. You can be able to draw beautifully and be horrible at tattoos or vice versa. To start in the tattoo business, you need to find a shop that is willing to take on an apprentice and start there. They will have you learn the basics.

The suggestions I've seen have included most to all of the following:

Learn to draw. Painting and other skills are useful, but real tattoo artists are excellent drawers/sketchers. You need to be able to do this for custom work. Sure, you can just copy flash & trace, but that's not recommended.

Take classes in art, ideally getting (at least) a BA in art. An MFA wouldn't hurt but isn't required. The woman who works on me has been an artist for over a decade and is talking again about returning to school for her MFA.

Build up a portfolio of your artwork. You'll need this to present to a tattoo place to see if you can apprentice under one of their artists. Finding an apprenticeship might take a while, and you might have more mundane activities for a while before you begin to work doing tattoos.

I suspect there are other ways into the field, but from what I can discern this is considered one of the more optimal (if difficult) paths.