Asteroid Fields can be found throughout the ESG Universe. There are 4 different types of Asteroid Fields (Cordite, Tritanium, Ice, and Aluminum). Each Asteroid Field can be mined to aquire their respective Ore.
To mine an Asteroid Field for Ore, simply shoot it with your ship's default attack (Spacebar). Every time a shot hits, there is a chance for a piece of Ore to spawn and float a small distance from the area that was shot. Eventually, an Asteroid Field will be destroyed, but as of version 2.6, simply docking and then undocking at any Space Station will respawn the entire Asteroid Field.
There is also a running List of Asteroid Fields being maintained by players, for players.