Instructions
Build eight Shipyards on your Home Planet. The Shipyard is a basic building used to make a variety of ships. Upon completing your eighth Shipyard, you will unlock the Warp Drive technology. This will allow you to control an Outpost Ship from the Shipyard.
Build an Outpost Ship from the Shipyard. The build time of an Outpost Ship takes a little over 2 real-world hours. Once it is finished, you will be able to control the ship, which can explore a majority of the galaxy.
Travel to another planet that is uninhabited. (When you approach a planet, many of its details will be displayed, including whether it is already inhabited by another race or another player.)
Click the build base option from the Outpost Ship. You will instantly capture and colonize the planet.