The colony ship. Can you pen the shipyard.
You have to research the tech to be able to attack.
to move a ship with a mouse can you left click on it. If you can right click where you want to go.
Also in order to colonize a planet it has to have a class better than one, and it has to be Terran in the beginning. There are two one other type it can be. This varies depending on who your race type. The other options are unlocked depending on what you research.