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After you dock out from the station, right-click on empty space, and select Asteroid Belts in the drop-down menu. You can choose any asteroid belt from the list, then select “Warp To” and the desired distance from the asteroid belt at which you will exit the warp (60 km to begin with, so as not to fall into the clutches of potential NPC pirates).
After arrival to the belt you'll already see the asteroids. Iinformation about any asteroid is available by clicking the right button and selecting “Show Info”. This window is only important to find out the type of ore available for extraction on a particular asteroid. If you're doing the training, even the type of ore is not really important.
Next, come close to the chosen asteroid no farther than 10 km, and lock the target (“Lock target”). If the asteroid is locked and you are farther than 10 kilometers, you will need to approach it (“Approach”). Then you can already activate the mining laser (if you have two of them – activate both) by clicking on it with the left button. If everything is correct, then the image of the laser will turn green.
After 10 seconds the laser will satrt working. Automatic extraction of ore is turned on by clicking on the laser icon with the left mouse button + CTRL. In this mode the laser will be mining until the entire hold of the ship is completely full. The laser is turned off by selecting “Deactivate laser” from the contex menu (for any object in Eve the context menu invoked by right-clicking on it), or by clicking with left mouse button on the laser icon if it is activated (green).
If the ore-bearing veins on the asteroid are depleted, then the hold may get only part of the planned amount of ore. The amount of ore you have in the hold can be checked by clicking on “Open my cargo” in the ship's context menu.
That's basically it - ore mining usually takes place peacefully and a bit monotonously; after the hold is filled up, you return to the station. The only thing that can be a threat for you during such a production is pirates, both players and the NPC.