First the 4x4 beams need to be cut to the size of the existing roof so the porch roof and the edge of the existing roof will be even when the job is complete.
Tying a porch roof into existing roof.
Butt the first new truss against the old one.
You have to do it thoroughly so that the rafters sit flush on it.
Attach the horizontal beam by using a nail gun.
After that to make it flush with the roof of the existing house cut the two outer rafters.
Tying a patio roof into existing house.
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I would frame a wall up flush with the brick and then use siding to cover it from there on up.
That fascia should be cut off where it is inside of the porch addition.
Tying in to an existing gable roof.
Now take the 4x4 beams and erect them to the perimeter outside the porch about four feet apart.
When a shed roof ties into an existing roof the new roof could be a simple lean to that covers a deck or porch or it could be the shed roof of a substantial addition.
Make a cutting on one of the sides of the horizontal roof beam on an angle.