Basically, it can be as easy as just adding the references to the ship entities into your race's build list. If you open PlayerTech/Psi/Phase you'll see it has a list for all the ships in their frigate and capital factories.
It gets more complicated for ships that require research, since you also have to make sure your race can do the research to unlock that ship. But that's done similarly also - just plug the name of the research subject entity into the playerrace entity file in the research block.