Climb the ladder and remove a section of vinyl siding from the house above the carport with a zip tool -- remove the section that will run the length of the carport. Slide it between the section to remove and the one above it. Pull down on the upper section until it unlocks and the piece you are removing is exposed. Remove the nails and the siding.
Draw a line on the house wall 4 inches above the frame, then measure and note the distance from this line to the top of the carport frame on the far side from the house; this will be the length of the support beams you'll install. Hammer a nail into the top of the outside frame and another opposite it on the line you've made on the house. Tie a piece of twine between them.
Measure the angle of the twine from the outer frame to the house with a protractor or an angle finder; this will give you the angle for the support beams you will install.
Line up two of the 2-by-4-inch lengths of lumber with their ends together. Move one so that the angle between them is the angle you measured with your protractor. Lay a carpenter's square across both pieces of wood at the end and draw a line across the wood you've just moved. Cut the wood along this line. On the top and bottom edges of this cut piece, measure and mark the distance you noted between the car port frame and the house. This will be the first of the support beams.
Use the measurement as a template to create more; the number will depend on the length of the car port. Bolt in place on 24-inch centers along the top of the car port.
Cut and fit sheets of plywood over the support beams to create the wood canopy. Work outward from the house and along the length of the carport. Screw the plywood to the support beams, placing screws every 6 inches along the beams.
Roll out a length of tar paper as long as the car port. Nail in place on the canopy. Nail a second length in place, overlapping the first by 4 inches. Continue with the tar paper until you've covered the entire plywood canopy, being sure to trim the tar paper at all the edges.
Nail flashing where the wood canopy meets the house. Bend the flashing to give about 1 inch above the canopy and 1 inch along the tar paper.
Nail the shingles in place with roofing nails, starting at the outer edge on the canopy and finishing where it joins the house. Brush a layer of roofing cement where the shingles meet the flashing, and once that's dry, caulk along the top of the flashing where it meets the siding.