Tip #1: Download
CPMA and practice with Promode physics. If you can play that, VQ3 is like walking when you could be running.
Tip #2: Quake 3 is much more about movement than aim. If youre a pro at Counter-Strike, chances are youre not cut out for Quake 3. If youre dedicated, learn how to strafe jump, circle jump, plasma climb, rocket jump and bunny hop. After you get movement downpacked, aim becomes much less of an issue
Tip #3: Its been eight years since Quake 3 was released and, by this time, people have scoped out the five or ten best maps on the planet - learn them. The more common duel maps include ztn3tourney1, pro-q3dm6, hub3aeroq3 and q3tourney4.