Cut away any insulation and caulk left on the wooden frame in the window's rough opening using a 1/2-inch chisel and a hammer. Test fit the new window in the rough opening. If the nailing fin (the metal lip around the window's perimeter) doesn't come into contact with the wooden frame around the entire rough opening, you need to make the frame thicker.
Measure the rough opening's length or width (depending where you need to add thickness). Transfer this measurement to a 1-by-4-inch pine board. Cut straight through the pine board at the measurement mark with a miter saw.
Position the pine boards within the rough opening. Drive 1 1/4-inch wood screws through the boards and into the wooden frame with a drill and Phillips driving bit. Position these screws in pairs every 4 to 6 inches.
Lay the new window face down on a pair of sawhorses. Insert a tube of silicone caulk into a caulk gun. Squeeze a bead of caulk along the window's nailing flange, around the window's perimeter.
Lift the new window into the rough opening from outside and center it. Press the nailing flange tight against the wooden frame. Return inside and set a level on the window's sill. Insert wooden shims underneath the window (between the window frame and rough opening) to lift the low end higher to make it level. Cut off the portion of each shim that extends past the window with a utility knife.
Return outside and hammer galvanized nails through the nailing flange and into the wooden frame. Some nailing flanges have manufactured holes to drive the nails through. If your flange does not, center the nails over the nailing flange and space them 4 to 6 inches apart.
Fill any gaps between the window and brick siding with expanding foam insulation.