Install metal flashing along the line where the wall of the original house meets the roof of the addition. This flashing should extend at least 10 inches up the wall and 10 inches out along the roof. The flashing must be underneath the siding on the wall and the shingles on the roof.
Cover the roof sheathing with tar paper, then shingles. This will give you an extra layer of protection from leaking if any water manages to get through the shingles.
Lay a row of shingles at the bottom edge of the roof with the tabs pointing up instead of down. Lay another row of shingles directly over them with the tabs pointing down. This method prevents water from seeping between the tabs at the eaves and eventually rotting the sheathing on the roof.
Insulate your attic thoroughly. A poorly insulated attic will cause snow to melt on the roof and run down to the eaves. When it gets out onto the overhang, the water will turn to ice and create ice dams along your eaves. These ice dams cause water to back up under your shingles and can cause leaking.