Measure and mark the window opening on the inside of the brick wall. Place tape on the wall to outline the cut you'll make as a guide.
Dig the dirt from the side of the wall if you're cutting into a basement wall that is partially underground. Dig down at least 6 inches lower than the proposed window opening to give yourself plenty of room.
Drill holes through the wall from the inside to the outside using a hammer drill. Drill the holes at each corner of the proposed window opening. Ensure that the holes go all the way to the outside, as they will be used as a guide for marking the window outside.
Measure and mark the window opening on the outside of the wall using chalk or a grease pencil. Use the holes you drilled as a guide to place the window opening.
Cut a shallow 1/2-inch cut around the window opening on the inside of the wall using a concrete saw fitted with a diamond blade. Make a second pass with the concrete saw to make the cut deeper (between 1 and 3 inches.)
Cut the bricks on the exterior of the wall in the same way using the concrete saw. Start with a shallow cut, and go back over with a deeper cut.
Break away the blocks inside the window area using a hammer. Pound carefully along the perimeter of the window to ensure you don't damage the bricks that are remaining in the wall.
Smooth the edges of the window opening using a brick chisel and hammer.