Inspect the existing membrane for any tears, cracks or other defects that could allow moisture penetration. Repair or replace any defective material. Check the underlying roof decking to ensure it is solid and firm. Measure the roof with a tape measure to determine the square footage for the number of foam board panels needed; foam board typically comes in 8-foot sheets, either 2 or 4 feet wide.
Get unfaced foam board of a type specifically designed for installation over waterproofing membrane; using board with a moisture barrier facing will allow condensation to build up within the roof, creating dampness problems. Buy foam board with tongue and groove connections, if possible, preferably a style that has drainage channels built in so any moisture that does get in will drain away.
Fasten new foam panels, with drainage channels facing down, with broad-headed galvanized shingle nails. Drive them with a hammer with the head flush with the top of the foam. Avoid compressing, denting or dimpling the foam. Space nails to conform to the rafters or trusses under the roof decking.
Cut panels to fit as needed with a utility knife or drywall saw. Secure seams of foam board panels with tape from the same manufacturer. Lay tape over each edge of two panels and press it firmly into place. Cut to fit with a utility knife.