In order to invade a planet, you need the following:
- Tech: Planetary invasion
- Ship: Transport (the game has one template of a Transport but you can also design your own kind in the shipyard)
- An enemy: On the whole, you can only declare war by actually going to war. You attack a ship, starbase, planet and the game will inform you you are about to commit an act of war. Just click 'yes' and you have your enemy. Invading a planet is considered an act of war too.
- An undefended but inhabited planet: you can see whether the planet is defended by the shield icon that will appear near the planet. If the shield is present, you will first have to clear the guards by attacking the planet with your own attack ships and repeating the process until the shield disappears (the guards are gone).
- Managing your transport: it works pretty much like colonizing a planet. You launch the ship, pull soldiers/taxpayers (they're the same for this game) on board and move to the target. The difference is that instead of targetting an empty planet with a ship equipped with a colony module, you use a ship with a troop module and aim it for an inhabited planet.
Hope this clears everything up.