Asteroids are resources found in the space zones around each of the major planetory systems in the game. To mine asteroids you must have the RotW expansion and special equipment on your starship. You launch into space or hyper into the desired system and then find the asteroid locations on the "Space Zone Map" ("N" on your keyboard) Right click on the asteroid in the POI and get options to "pilot to" or "create waypoint to" the asteroid.
I really think it helps if a person is old enough to have been around when the original Asteroids game was around, liked it at the time, and now can really appreciate this new and improved version in 3D with a healthy payout at the vendors. Course a person would have to be willing to admit they're THAT old. Don't know anybody like that