What do AWT and Swing do which aren't done the best ways?
Well unless you're very careful and restrictive in what you're doing, most drawing is done on the CPU in software, which is never going to be able to compete with dedicated graphics hardware in terms of speed.
And how else do you do it? (Which is the same question CodexArcanum had, I guess)
Grab yourself an OpenGL binding (like
LWJGL ) and use that instead. Nice, fast, hardware accelerated drawing will all sorts of added extras you normally wouldn't be able to do with regular 2d graphics.
Isn't Fullscreen part of awt?
Dunno whether its tecnically part of AWT or Java2D, but yes its part of the regular java platform. It still seems to be somewhat buggy though from what I've seen. Of course if you use LWJGL you get its own fullscreen methods which tend to be more reliable.

Oh, and if you fancy giving OpenGL a shot, grab yourself a copy of the
RedBook