Good advice from all, but design ends in production of some kind. Knowing how it will be produced will make you an excellent designer for printers and others to work with, and make you happy with the results of your hard work. Unfortunately, most designers have little idea what is involved in actually getting the design onto something, resulting in a pretty but unworkable mess being handed to the production team. Having spent 25 years in commercial printing companies, silk screen companies and photographic studios, I have been the one to take these designs and transform them into workable form. Having another artist rework your finely crafted artwork can be devastating. You can avoid that with some knowledge.
Take a little time to decide what kind of design you want to focus on. Then get yourself a job in those companies and learn how your work will look once it is put through the mechanical side of production.
I am surprised that no one mentioned page layout programs. Lots of attention paid to Photoshop, which is grand for photos, but is not a page layout program.
Illustrator is great for vector art, general layout and design.
CorelDraw has gotten better and it’s files can actually interface with Adobe programs.
My favorite is QuarkXpress for page layout, Freehand for art elements, and, of course, Photoshop for photos.
Just learn all you can. A part-time job in a production environment would make it clear what things you need to concentrate on, and you get paid to learn!
Good luck!