A broken shingle is both ugly and a leak waiting to happen. But as long as you can find matching shingles (and you're not afraid of heights), the repair is straightforward.
Pick a day when the weather is moderate to do the repair—too cold and the shingles can crack; too warm and the shingle sealants are tough to break.
Loosen the tabs under the broken shingle and the next two courses above it (Photo 1). Shingles are fastened with eight nails each—four at the center just above the tab slots and four through the shingle above it—and you have to lift up all the shingles that cover those nails to remove them.
After all the tabs are loose, push the flat bar up under the damaged shingle to each nail, centering the nail in the flat bar notch (Photo 2). To avoid ripping shingles, gently work the pry bar under both tabs as you push it up.
Pop out the nails by prying underneath the shingle instead of trying to dig the nail head out from the top of the shingle; that will wreck the shingle. Then push the shingle down from the nail head and pull out the nail. After removing the center row of nails on the damaged shingle, lift the undamaged shingles above it and remove the next row of nails. Then pull out the damaged shingle.
Slide the new shingle up into place. Nail the center row first, then the center row of the course above it, nailing 1/2 in. over from the old holes (Photo 3). Nail at the top of the slots between the tabs, just above the sealant strip.