To colonize a system, you need enough strength on a system you control. The strength requirement is shown in the bottom left of a system card, along with its VP value. Note that the strength requirement may be altered by certain event cards.
If you meet the above requirements, next you have to take a colonization action on the technology board. It will likely cost both ore and people cubes.
The action will consume your ships. Those ship dice will be put back on your board with its square side showing.
You then acquire the system, along with its points and benefits. A new system takes its place on the board.