dabeaner NAILED it in his answer. I have been one for some time, but, like Richard Craig said, you've got to have some education credentials to get a job in that field.
I just totally redesigned my DesktopDirect.TV site, and I did all the web design and graphics myself. I'm currently working on ViralTrafficAnarchy.com and the graphics are coming easily.
If you're serious about getting paid, try developing some graphics or site templates and uploading them on GraphicRiver and ThemeForest just to see how you do.