You have to replace a few shingles.
How to repair small hole in roof.
Assessing a roof leak.
Repairing nail holes in a metal roof is an inexpensive alternative to replacing portions of the roof.
Repairing holes in a roof requires that you to go on the roof itself so if this is a problem hire a professional to do the repairs.
If your ceiling has a plastic vapor barrier between the drywall and the attic insulation push the insulation aside and look for flow stains on the plastic often water runs to openings in the vapor barrier such as at ceiling light fixtures.
Where are you going to get the new ones.
The hole in your roof is small and accessible your roof is basically sound and within its expected lifetime 20 years for an asphalt shingle roof you have solid knowledge of home improvement and roof safety plus a proper roofing ladder good non skid shoes and a buddy to assist you.
For a small repair i would guess that after a bit of clean up a patch is fastened from below and a filler is used to make things level.
Sometimes the water shows up at a ceiling spot distant from the leak.
Some overhead leaks are due to minor problems such as a single torn shingle or a small hole in flashing that you can usually handle with a little diy experience and some.
As to how the repair is made for the big repair i think the replace the odb sheet.
Hold it against the inside of the plywood by pulling up through the hole while driving deck screws through the roof and into the brace.
Smaller nail holes will be permanently fixed by this method standard roofing nails would be either 3 8 inch or 1 2 inch making a hole.
Apply urethane caulk using the caulk gun to the back of the.
There may be jagged edges left over from grinding or snipping away at the metal.
Use a ball peen hammer to tap the edges of the hole inward.
Use a jigsaw to cut a rounded shape from the plywood to the exact size of the hole.
Some roof leaks are tough to locate.
Fill small nail holes with silicone caulk or roof cement.