For creating vector drawings, Inkscape is an excellent, free application. The Inkscape tutorials blog hosts lots of excellent tutorials on how to draw and create all sorts of great effects. It has tutorials about text effects, drawing shapes and 3D objects. And if you have a tutorial you would like to share with the rest of the world, you can submit it!
Another good collection of tutorials can be found at Screencasters, wich has video tutorials. These are really great! Currently, there are 47 tutorials, starting with some very basic stuff and moving on to more advanced techniques. The guy who created them explains everything he does while he’s doing it, making it very easy to follow.
And finally, there’s the Inkscape Forum, where you can show off your work, post your own tutorials or ask for help if you’re stuck. It’s quite active, so you should have no problem finding help there.