Here s a great video that explains the process to repair your roof by replacing a missing shingle.
How to repair a missing roof tile.
Cracked or broken roof tile 1 carefully pry up the tile or tiles just above the cracked or broken one.
Also pry or force out any nails.
Lift the 2 tiles with wooden wedges.
2 break the faulty tile and remove the pieces.
In short you will need to replace the entire 3 tab shingle that was torn while protecting the integrity of shingles above and below the one being replaced.
3 spread a small amount of roofing cement along the underside of the replacement and slide it into place.
With roofing tiles it s common practise in large parts of the uk to fix every third row of tiles with clout nails starting at and including the bottom row every third row after that including the top row and they should be nailed with either galvanised steel aluminium or copper clout nails.
Finally hook the nib over the batten.
Raise the damaged tile off the bottom using a hand trowel.
Broken tiles could be removed and replaced by the following simple steps.