The ASTP docking module was launched munch like the LEM, inside the fairing between the Apollo CSM and the upper stage of the Saturn. When in orbit the A-CSM did a 180 degree turn, docked with the docking module and removed it from it container, much like the moon missions. The entire A-CSM and DM then docked with the Soyuz.
The strikes me as a method to resupply Skylab and attach a boosting rocket to Skylab. Surely NASA could rig up a rocket that an Apollo could attach to the 2nd docking port of Skylab and leave it there when the manned missions are finished. I'm assuming that the Saturn IB has the grunt to lift the A-CSM plus some rocket thingy to 500 miles at 52 degrees inclination. Or perhaps, with the serious rocket power of the A-SM it doesn't need to, the service module could lift the combo up to the full orbit.