To conquer new types of planets and mine new minerals on them, you need to learn the appropriate skills on your Orbital Station in the tab Skills.
Learning skills becomes available after accumulating the required amount of Energy and Solarium minerals for each skill. At least one building is required to learn spacecraft skills «Spaceport» on your planet.
There is only one class of ships in the game that can capture (occupy) planets - it is the Planetary building complex «Titan».
However, it is able to capture only those planets on which minerals are mined that have already been learned by the player in the tab Skills. Also, Titan can capture only free planets or planets of other players which do not have Shields and planetary «Missile towers».
There is only one class of ships in the game that can destroy planetary buildings of other players - this is the Planetary Bomber «Valkyrie».
There is a game Galactic market, where you can buy the necessary resources and ships.