Determine the pitch of the roof on the existing house. If possible use the same pitch on the room addition.
Set up and nail in place as many rafters as possible and the ridge board on the room addition. Use bracing to hold them in place. Make the ridge rafter level and extend it over towards the existing roof as far as possible.
Place a nail and attach a string to the top of the ridge board near the outside edge of the room addition. Take the other end of the string over to the existing roof. Sight down the string and move it up and down until it almost touches the ridge board of the room addition. Pull the string very tight to eliminate sags and do not let the string bend by touching the existing structure. Place a nail in the existing roof at this location and wrap the string around it several times to secure it in place. Use this same procedure in the middle of the rafters and at the bottom of the roof, on both sides of the roof.
Chalk a line on the existing roof from the top of the ridge board to the bottom of the roof edge where the nails holding the strings are located. Check that the nails are in a straight line from top to bottom. This will be the valley locations where the new roof will meet the old roof.
Slide a 2 by 6 foot or larger piece of lumber onto the existing roof underneath the string that are attached to the roof. Nail it in place underneath the attached strings. The top of the board should not push the string up out of place, but only lightly touch the string. The bottom of the rafters will be nailed to these boards.
Extend the ridge board and the rafters from the room addition over onto the existing roof. Attach them to the boards that were previously nailed onto the roof. Set the rafters with the same spacing all the way to the end.
Attach the decking material to the top of the rafters. Extend it over until it touches the existing shingles. Chalk a line one inch past the valley onto the existing roof and cut the shingles all the way through to the decking on this line.
Lift the existing shingles, remove some nails if necessary and slide the flashing several inches underneath the existing shingles. Nail the flashing sparingly on the outer edge away from the valley. Lift the shingles and place roofing cement underneath the edge of the shingles. Be sure to cover every inch from top to bottom with the cement.
Cover the room addition with shingles and underlayment if desired. Trim the shingles in the valley to match the existing roof.