Upon starting the game, you're presented with a menu. You can use the menu system to setup your screen resolution, player name, and controls. There is also an in-game server browser which you can use to find multiplayer servers to play on.
Aside from the menus, the Quake console is the other portion of the game's user interface you'll encounter. Press the tilde (~) key to toggle the console at any point in time. There you may enter commands to view levels offline, connect to servers, change your player's name and model, customize your controls, etc. See Client Configuration for more information on console commands.
To gain your bearings, try viewing a level offline. Type map torn to spawn into CardO's level Torn Glory. By default, the w a s d keys will control your players movement, and your mouse will control your aim. The Levels section contains a full listing of maps available for offline viewing and online play.