A bird's mouth cut lets a rafter sit squarely down on the top of the wall, rather than resting against it at an angle. For the rafter to fit correctly, you need to cut the bird's mouth exactly where the rafter will meet the wall. Once you've cut the top end of the first rafter, you can calculate the position of the bird's mouth based on the height and width of the roof, then use that rafter as a pattern to cut the others.
Measure or calculate the height of the roof from the top of the wall to the top of the ridge plate and multiply that number by itself. Measure the distance from the outside of one wall to the outside of the other wall, subtract the width of the ridge plate, divide by two and multiply that number by itself. Add those two figures together and take their square root.
Measure along the top of the rafter the distance that you calculated in the previous step and put a mark on the top edge of the rafter.
Measure the same distance along the bottom of the rafter and put a mark on the bottom edge of the rafter.
Draw a connecting line between those two points using a straightedge or one side of a carpenter's square. The line should be parallel to the plumb cut on the top end of the rafter. This line marks the plumb cut of the bird's mouth.
Draw a line at right angles to the bird's mouth plumb cut, starting 3 inches up from the bottom of the rafter but no more than half the thickness of the rafter. Use a square, placing one side against the plumb cut line. This new line marks the horizontal cut for the bird's mouth.