The best things to do are to draw and read! Take as many Art and English classes as you can while you are in school and see if you can find some Art classes through your local park district or community college children's programs. If you can't find any Art classes, then check out Art books from the library and study them. Go to museums and look at the artwork there - much of art history is really illustration
Spend a lot of time at the library, looking at children's books and magazines, both old and new. Look at the pictures and decide what you like and don't like, how are books different for little kids and older kids, how could this picture be better? When you go to college try to find a school that has a good illustration program but also plan on taking other classes, too.
You need to know some math and business to do your own record keeping, history to give you a good understanding for illustrating other time periods, science if you are interested in drawing people or animals. English classes are good especially if you want to write your own books some day.
Working in a library, or a bookstore could be a valuable experience for you. Some libraries take young volunteers to do work at libraries, you might ask your school or town librarian if there is anything you can do to help them.
Carry a sketchbook with you all the time and draw from life. Copying from books and photos is a good way to get started but eventually you will want to be able to draw using your own ideas. You need to be able to draw people of all ages, animals, buildings, landscapes, furniture, all from different viewpoints and perspectives.
Most illustrators get started by slowly building up a portfolio of their highest quality work, then sending out samples (never originals) to publishers. Ask your librarian if they have a copy of the current edition of Children's Writer's and Illustrator's Market - there are some young author and young illustrator markets listed in it. Most of these don't pay anything but they would be a good way for you to get experience in being published.