Most General Motors vehicles (Buick, Cadillac, Chevrolet, Hummer, Pontiac, Saab, Saturn, etc) with direct TPMS systems learn new sensors manually. Typical method for initializing learn mode is by turning the ignition on and holding the lock & unlock buttons on the key fob until the horn beeps twice; then a TPMS tool can be used to trigger the sensors for registration. On newer models, learn mode can be initiated through the dash display using the steering-wheel buttons. A TPMS relearn should be performed when rotating tires or replacing sensors.

Potential problems with manual learning: horn doesn’t beep when testing sensors, vehicle picks up a sensor emission from a nearby car, and RKE issues (key-fob was lost, has a low battery or only an after-market unit is available). If sensor learning is started but not completed, then the module might clear the stored IDs for all sensors.

If the horn doesn’t beep when the sensors are triggered, then technicians can roll the window down or drive the vehicle forward a few feet and try the relearn again. Also moving to an area with less RF interference and away from other vehicles might help.

For other issues with manual relearns, OBD-learning and OE cloning are options.
There’s no time limit when learning via OBD, and it’s the same process as other vehicles (Honda, Toyota, etc). The IDs are written directly to the ECU so it’s not possible to learn a sensor from a nearby vehicle.
If the original sensors are cloned, then the relearn can be skipped. Cloning OE sensors can be done by either testing the OEM part (ID copy) or by manually entering the ID numbers into the tool when programming sensors. A guide that shows how to find OE-sensor IDs is available here.