Rappel is a descent system with a backup, not a rest. Most of the people who die on rap skipped a backup or unclipped the last clip too early.
Manufacturer box
A GriGri used to rappel a partner-style rope is within Petzl's rappel technique pages. Using the same tool as a lead-solo belay is not. Petzl: rappelling with GRIGRI and NEOX. A GriGri rappels on a single strand (blocked at the rings, or a fixed line). It does not rappel two strands the way a tube does. Read the sheet for your device. ATC / Reverso rappel is a different manual.
Procedure
Stay clipped to the anchor until the rappel is threaded, backed up, and weighted.
Extend the device off the belay loop (PAS or sling) so you can reach the backup.
Backup below the device on the brake strand (autoblock / third-hand, or a second device you know how to tend).
Knots in both ends if you could rap off them. Stopper above a knot you must pass — see Self-rescue.
Weight the system. Then unclip from the stance.
On a lead-solo pitch: the lead device comes off only after this rappel is holding you. Same order as multi-pitch solo.
Stuck rope
Do not keep yarding until the sheath melts or a block comes off.
Try the other end, a different pull angle, or walking the line if the terrain allows.
If it is stuck at the rings, you may have to climb back up a remaining strand with a backup — that is a rescue, not a shrug.
Prevent it: do not rap over a flare you cannot see, and do not leave a knot that cannot pass the rings if you meant to pull.
When this system is the wrong tool
You still need to lead — rappel is not a belay.
One strand, no backup, and a tired brake hand.
A fireman's belay from below only exists if someone is there.
Self-check this system
The learn page has a mistakes list and a quiz built from this guide. A high score is not training.