You control the ship by clicking on it, keeping the mouse button clicked and dragging the mouse. This will change the speed of the ship so you can control its trajectory.
If you want another game that has similar control, check out Kerbal Space Program, especially the map view.
Without a tutorial or experience with a similar control scheme there's no way you could just guess it.
Regarding the mechanic: The goal is to make the ship go through the targets (the green circles around planets), by changing the speed of the ship as little as possible.
Anyway thanks for taking the time of checking this game out.