This section is from the book "The Carpenters' Guide", by Harvey Miller. Also available from Amazon: The carpenters' guide.
Nail a shingle at each end of eave to be shingled and let them extend 1 1/2" or the desired distance over the sheeting for the drip. Put a shingle nail in the end of the shingles and draw a line taut across the eaves. Then lay a double row of shingles to this line, being careful not to allow the shingles to move the string out of line. Leave about 1/16" between line and shingles to prevent this.
Measure up from the lower edge of shingles 4 1/2" or 5", according to pitch of roof, for second row, and strike a chalk line for 3 rows. Shingle and continue this method until roof is covered (fig. 45), putting two nails 5/8" from the edge in a shingle. You may use a straight edge to lay the shingles by, moving it up for each row. An expert shingler usually uses a gauge on his shingle hatchet, and lines with chalk and line every sixth row instead of using the straight edge or former method. Let shingles project over the gable facier or mould 13/16" of an inch.
To cut a valley shingle to fit the valley or hip, take the hypotenuse of the base and rise of the common rafter with the base, 12", and mark on the length of the hypotenuse. (Fig. 35.) This rule is reliable for hip or valley shingles. The end of the shingle cut from the valley will make a hip shingle. Do not have two cracks directly over each other. Keep them 1 1/2" apart for a good roof.
Chalk line the valleys to lay the shingles in line, leaving 2 1/2" valley between the shingles. It is advisable to have the top of valley 1/2" narrower than the bottom. The valley tin 14" wide, laps over and down.
To estimate the number of shingles for a roof, take the length of rafters and the projection of the gable and find the number of square feet in the roof. For 4 1/2" to the weather it will take 9 shingles to the square foot; then 9 times the number of square feet is the number of shingles required, and other widths in proportion.