Destroy all enemies in the area. To destroy huge objectives like ships or bases, eliminate all of shield generators (red-light-blinking hemisphere object). After you accomplished the mission, the booster ship will drop out of the hyperspace. Dock with it to refuel and proceed to the next stage.
The shield increases gradually by consuming energy. You'll be destroyed when the energy runs out or you are hit when the shield is low.
If you lose much energy, the booster ship appears and you can refuel once in a stage.