You should have a look at
ICAO Annex 10 for more info on GBAS. It gives a good description of how the approach path is defined. For GBAS it is uplinked to the aircraft from the ground station.
The aircraft derives a differentially corrected 3D GPS position so both lateral and vertical position is provided by the GBAS. Typically the GBAS receiver and processing equipment will be contained within an MMR with guidance outputs to the autopilot/flight director. The GBAS approach can be selected through the FMS or through a separate control head, just like selecting an ILS approach.
If you need more info try Googling "GBAS" or "LAAS".
Cheers, NM.