Simply dominate an enemy in a war whatever way you want until you can move about freely. At this point you either build or reconfigure ships to carry groundtroops. These can only be build or upgraded in a system of yours, that has enough extra population, since groundtroops are made up of your population. Go figure that.
After having at least five fleets, enter 5 different enemy systems, check if you have a high enough chance to conquer them and then... well, conquer them.