Design and other professions can be selftaught without any problem as long as you know what to learn and have time to practice and master.
Since design is a very large area, I assume you want to learn how to design stuff that would be later in Internet, so it will be better to learn (in this particular order): typography & grid systems. Then color systems. When you master these areas, you can go to the stadium of the composition with color and form, where you will learn to draw.
90% of the design of an application go through the use of typography, the arrangement of elements on the screen using grid systems and interactivity of these objects. The rest is cosmetic. You can master cosmetics later learning to copy styles and practicing to the point you master them. For example, being able to illustrate, in this case, it's a matter of drawing, not doing extreme typography use, but that's another area of design and it will requiere grid to illustrate well, colors to give illustration deepness and etcs.
Go to amazon and search books on these matters, get inspired and start the selftaught process.
[1] http://www.amazon.com/Design-Hackers-Reverse-Engineering-Bea...
The same author has a whole series of books, some oriented specifically at the web.