There are many places that flashing can leak on your roof. Sometimes you can tell where the leak is entering; but, water has a way of moving around so you need to go up and inspect it. It's always best, if you are on the roof anyhow, to inspect all places that the flashing is attached and recaulk if necessary.
Check the drip-edge. Make certain that the seal between the shingles is good. If not, use roofing cement sealing beneath the shingles along the drip edge but not along the eaves. Put the cement about 6 inches under the edge of the shingle and spread to cover the drip edge flashing.
Inspect the valleys. Lift up the shingles that are close to the valley flashing and put urethane roofing cement on the area making certain to go under the shingles about 6 inches from the edge.
Seal vent (the support for the pipe that comes out of the roof) flashing. Using a filled caulking gun, place a generous bead between the vent pipe and the flashing. Take a dollop of roofing cement and generously spread it under the surrounding shingles. If there is a flashing flange, next to the vent flashing, make certain to fill the seams in between the two.
Check all areas around the chimney. Connecting the flashing to the chimney there is mortar and caulking. Use a hammer and chisel to remove. Clean away the debris and caulk between the cap flashing and the chimney. Use the roof cement around the step flashing and the cap flashing.
For a dormer there are edges that need flashing also. Remove old caulking along flashing with a chisel or screw driver and recaulk with roof cement or weatherproof caulking. Gently lift the shingles and caulk under them. Recaulk seams in the flashing.
Look at the flashing around the skylight. There is a metal girdle on the skylight box called a flange; lift the shingles and spread roofing cement under them and over all joints up to that flange.
When using roofing cement, the type in a tube used with a caulking gun works best.
Be very careful when lifting shingles, so you do not cause damage.