Lay tarpaper over the roof. Start at the bottom of the roof and lay sheets of the paper, securing with staples every 6 inches or so. Overlap the edges of the paper as you go.
Begin laying your shingles at the edge of the roof. The first row of shingles should overlap the edge of the roof by around 1/8 inch, but they should sit flush side-by-side rather than not overlapping. It may be beneficial to measure and make chalk lines to keep this first row even.
Nail three roofing nails evenly along the top edge of each shingle. You may need to ask a friend to hold the shingle down around the curve of the roof so you can nail it down flush with the roof.
Dab a small amount of roofing putty over the head of each nail. This helps keep the roof waterproof.
Install the second row of shingles above the first. Offset this row so that the center of each shingle lies over the joint between two shingles on the first row. This offsetting helps prevent leaks as well. Overlap the first row of shingles by approximately 1/4 inch, so the shingle above hides the nails below.
Continue installing rows of shingles up the roof in the same overlapping, offsetting manner, following the contours of the roof. Use extra nails if necessary to keep the shingles flush with the curved roof. As the roof is curved you won’t need to cut shingles for a roof ridge. If you need to, trim roofing shingles to fit the shape of the roof with heavy-duty shears or vinyl cutters.