It really does depend on what you want to do for a living, but if you REALLY want to work in art in some way, do the following:
GO TO ART SCHOOL.
If you really want to work in the graphic design or animation field, you need a degree in art to go to a specialized art school. The fact that you did go to school to learn you're trade looks great on a resume to potential employers, or just as part of the track record.
Now, since you want to work in animation, you really should be buying anatomy books and still-life books. These will help you study the form and shape of people and objects. Also, really study perspective, learn about distance and the horizon line, etc. this stuff is absolutely needed for animation.
You also need to be versatile, to be able to draw and work in different styles and/or mediums. You'll probably start working as a grunt-animator on a project, so you need to understand the director and animation director's style to make the frames YOU drew look exactly like something they would draw.
If you work in graphic design however, you really should find a style all your own. Look at all sorts of art, from comics to classical to post-modern and pop to see what artists inspire you to create. also think of what medium you want to work in. Do you want to paint? Air-brush? Use a computer? These are all things you need to decide and experiment with.
Good luck! I hope you become a billionaire!