The best way to start the game is in the practice mode. Practice some of the tournament maps, and learn how to fight.
There are several map types in UT 1999:
If you who like hardcore gaming, you can play Last Man Standing Botmatch, then press to bring up the console. Type Addbots 300 to add 300 AI-controlled bots for you to duke it out with. A higher-end processor may be required.