How to build a Colony Ship

the colony frigate is built from a frigate factory

for advent its the missionary vessel, for vasari its the jarun migrator, and for tec its protev colony frigate

each faction also has a capital ship capable of colonizing, built from the capital ship factory

for advent its the progenitor mothership, for vasari its the jarrasul evacuator, and for tec its the akkan battlecuirser

For the colonizer capitals, you will need to assign at least one skill point into the Colonize ability, otherwise your capital ship will not be able to colonize planets. Higher levels of Colonize provide shorter cooldowns between colonizations, and improvements to the bonuses newly colonized planets receive.