Resources and ground units can be moved between planets in transport ships. The primary method for moving resources is trade routes, which do not require transports. However, trade routes have a maximum range of 200 LY and will not move ground units.
Resources and ground units can moved between an existing fleet and a planet with the transfer interface, or included in a new fleet generated with the deploy interface. Both the planet and the fleet must belong to your empire for this to work.
The two transport ships currently in the game are both jumptransports and require jump beacon coverage to move at full speed. They can perform transportation beyond beacon range if they are part of a mixed fleet.
Both classes of transports have a per-unit cargo capacity of 20 kt. If an carried unit or resource has a mass >20 kt, it will be split between multiple transports. Cargo continues to undergo attrition within transports and when transports are lost to attrition any cargo they carry will also be lost.