Examples, a building is 24 feet wide, a 12 foot run. and teh slope is 6 in 24.
Mark the plumb cut by setting the square on one end of the board. As this is a 6 in 12 roof. the tongue the narrow part interects the edge of the board at the 6 inch mark, and the blade, the wide part at the 12 inch mark. Hold the square this way and make all the marks.
Determing the rafter length with the formula a2+b2=c2, a and b are the rise and run. Or look at the tables stamped on the blade of the rafter square. The 13.42 under the 6 inch mark means that for every inch of run, you need 14.42 inches of length. If the run is 12 feet the rafter length for a 6 in 12 roof is 161 inches or 13 feet 5 inches.
Measure down from the plumb cut a distance equal to the rafter length and mark the top edge of the baord. Holding the tongue of the square against this mark, set the square so that it is 6 inches 12 and scribe a line.
Slide the square in its 6 in 12 position, back toward teh original plumb cut until it creates a line for the seat of the birds mouth that is exactly the width of the cap plate. Mark that positin.
Mark the tail cut by sliding the square beyond the birds mouth the distance of the overhang.
Move the mark for the plumb cut toward the birds mouth. The distance shouldb e exactly one half the thicknes of the ridge board.
You need pictures to understand how this works, but if you can visualize this example, you can see how it works for rafters, Stringers are the same way, but much easier.