You can explore or attack, or use an Artifact (Planetary Core capsule)
To Explore, (which is what you should do becuase you probably dont have the money nor research to support a fleet) build Scouts
Then go to Explore
Then spend some turns exploring, and it will tell you when you get a planet, and colonize it, becoming your colony
I suggest reading the Getting Started Guide, and the Manual in general
it will help you out a lot with these basic functional questions