In order to conquer a planet, the principles are more or less the same as in ship-combat. A planet, Moon or asteroid has a lot more “health” than a ship. Planets under a faction will have weapons and additional shields depending on how many people invested in them. So it is best to go in a group or to be very patient. If that planet has no faction owning it is just a matter of going down. A few NPC’s may target you if agressivity is active! You will be shot at from the location you are attacking and surrounding locations if you are within the range of the defences they built if that system is under faction control. Every Planet, moon or asteroid under that faction you attack will attack you within the range of its weapons.
You just “Move to orbit” once you are above the planet or within 100 mkh you open fire until the health bar of the planet is red. To be sure you shot it all check your chat. If it says 0 damage done. It means the planet is fully emptied out of health. YOUR SHIP CAN ONLY SHOOT THE PLANET IF IT HAS BOMBS ON BOARD. If it has no bomb module it can’t bomb the planet. Normal weapons can’t shoot them!
Either a friend or yourself come back with a “Builder”. You don’t need minerals to terraform a planet for your faction. Once you are in orbit of the planet you press “Terraform” in the weapon systems section. Once that is done you will have to wait/protect your planet for up to 10 minutes. Congrats! The planet belongs now to your faction and gives you hourly income(faction-wise).
You can see to what faction planet belongs if you click on the planet it will show up under its name/range.