Rip off the old roof shingles with a crowbar or shingle shovel tool. Remove all the damaged or puckered plywood with the crowbar and discard.
Lay the new plywood on the roof starting at the lowest point, which is typically at the bottom of the roof. Nail through the plywood and into the framing for the roof at each roof joist. Space nails about a foot apart along the joist for the best installation.
Space the next board 1/8 inch away from the first all along the edge using a 1/8-inch spacer. Nail this board to the roofing joists in the same manner as the first.
Continue to install the plywood to the roof using the spacers and staggering the plywood sheets so each row overlaps the previous one by half. Measure and cut the plywood boards on a table saw to achieve this stagger effect. Replace all damaged plywood boards until the roof is completely covered.