How should residential roof flashing be installed to prevent leaks?

Residential roof leaks are often not caused by the tiles or shingles themselves, but by flashing details that don't follow the water flow. At chimneys, skylights, wall junctions, and roof ridges, water doesn't just flow straight down; it slowly creeps through gaps. I once saw a roof that started leaking six months after completion; after tearing it open, I found that the step flashing and siding…