You're piloting a spacecraft in an enclosed, vaguely donut-shaped arena populated by other ships which can either fire at you or lay mines in your path. You must avoid colliding with either enemy ships or mines, which can be tricky since your vehicle is in zero gravity -- too much thrust, and you may not be able to get out of the way. You advance by blasting enemies and obstacles off the playing field and moving up to the next level.
Omega Race was originally a Bally/Midway arcade game, and was translated for the Atari 2600 by CBS Electronics, which had an overall licensing agreement to port Midway games to home consoles. This version of Omega Race is unusual in that it's one of a very small number of Atari 2600 titles which includes its own specialized controller. The Booster Grip is a two-button controller which slips over the standard Atari 2600 joystick, adding a trigger and a thumb button, both of which control your ship's thrust in Omega Race. (If any further games were being planned for use with CBS Electronics' Booster Grip, they never saw the light of day.) The Atari joystick plugs into the Booster Grip, which then plugs into the console itself. (The joystick's existing button is used to fire.) Since many used copies of Omega Race change hands minus the Booster Grip, beware: The game is absolutely unplayable without it.