Establish a Trade Gate contructs, which is withing 4 legs of your homeworld and any compatible planets will automatically get colonised by your noble race. They are colonised at a rate of +1 per galactic turn. If the gate is destroyed then they shrink at a rate of -1 per galactic turn. Compatable planets are listed with a potential maximum population of 5 or more.
The number of legs - or RipCurrents as they are also known - between a system and it's homeworld is shown by the game client.
The goods raised by the colony are the same as the population of the planet. However, the number of legs from the homeworld will result in a taxation level. See the economy section
Your home planet can never be attacked and generates 0 goods for you each turn. Note that other players may share your home planet - being of the same race. Think of them as differing nations.
Colonies get taxed - see the RipCurrent section for details. It is worth highlighting that colonies in open systems (those with more than 10 planets) get taxed at the 2 leg rate AND also act to continue the RipCurrent network - by up to another 2 legs.
Colonies of size 5 and more can also repair habitat if your ship is in thier GravWell. They send short range shuttles up to the ship with new crew aboard.
Simply move your ship into the planets GravWell and click on the damaged habitat as normal to do the repair.