Mark spots on the top and bottom of the wall indicating where the studs are located. You should be able to do this by locating where the old siding has been nailed in place.
Install the fan-fold foam insulation over the existing siding by temporarily nailing the boards in place at the corners. Using the chalk line and the marks showing where the studs are, mark vertical lines on the foam board. Permanently install the foam by nailing it along the lines into the studs.
Find the low point of the house by using a level and chalk line. Following the siding manufacturer's instructions, use the chalk line to mark a base line at the height indicated above the lowest point. Fasten a starter strip to the house at this line.
Install inside and outside corner pieces. Because vinyl expands and contracts with temperatures, do not hammer nails tight -- leave about 1/32 inch of space beneath the heads. Also, leave 1/4 inch beneath the eaves, and extend the corner pieces 1/4 inch below the low point of the old siding. The siding will fit into these pieces and hide old siding, with room to expand.
Install J channel around the edges of doors, windows and non-removable obstacles and along sloped eaves. Install undersill channel on the undersides of windows and under horizontal eaves.
Install the siding pieces by starting at the base, setting the bottom of the first length of siding on the starter strip. Nail the siding panels through the pre-punched slots. Hammer the nails through the center of the slots, and don't forget not to hammer the nails tight. The siding should be secure, but leave enough room for expansion.
Check the strips for level installation every five lengths and make necessary adjustments.
Overlap adjacent panels by 1 inch, and stagger joints by about 4 feet. For shorter sections of wall, avoid joints altogether.