To be able to colonize your first planet, you will need to developp your colonization technology. To do so, you'll first have to get those : Research Lab lvl 2; Astrophysics lvl 2; Microelectronics lvl 2.
Once you unlocked the colonization technology, you'll be able to upgrade it, and every three levels will allow you to get a new planet.
Getting a colony ship is the second step of the process. To get it, you will have to unlock : Shipyard lvl 4, Impulse engine lvl 3
Once you've built your colony ship, all you need to do is choose the coordinates of your new planet and go get it !
Once you have your colony ship, go to your galaxy view (1), then choose location of your new planet and click (2) :
Firstly, select your colony ship and “continue”.
Then, check the coordinates. And now you can send it.
Your colony ship is now flying. Once he reaches his destination, you'll be able to see all your new planet's characteristics.
ATTENTION : If you receive this error message, it means you do not have your colonization technology high enough to get a new planet.