Create a large portfolio of artwork. Create original characters and drawings instead of making copies. Keep practicing anime and updating the portfolio. Ensure it only contains your best material. Keep all samples of your work as the size of the portfolio you will have to submit in the future will vary.
Enroll in art classes in high school. Even if they don't address anime or manga specifically, art classes will keep you drawing and introduce you to general drawing concepts that can be useful.
Learn Japanese. There are very few opportunities for anime artists outside of Japan. A person seriously pursuing anime may have to relocate there.
Enroll in a college art program in Japan that teaches anime. The program will not only hone your craft, but allow you to network and make connections that can be useful in getting work as an anime drawer. Large production companies may also keep an eye out for talent in these programs.
Upload your best work on Pixiv.net, which is where many aspiring Japanese anime artists upload their portfolios digitally (see Reference 2).
Get published in manga periodicals, such as "Jump." Many aspiring anime drawers try to get noticed through manga, which are the equivalent of anime comic books. You can also read "Bakuman," which is a manga about artists trying to get started in the business (see Reference 3). Many people start as Doujinshi artists, which means they create their own mangas and try to get them noticed.
Showcase your work at large comic and anime events such as Comiket (see Reference 3). Such events give aspiring anime artists a chance to get discovered.
Take an entry-level position at a production company. Make connections and wait for the right opportunity to present your portfolio.