Pull the vent cover off the pipe of a fan vent. Set the pipe aside. Hold the vent cover against the brick wall. Pull a piece of soapstone along the outside edge of the pipe extending from the back of the cover to mark a border on the brick. Set the cover aside.
Lock a 3/16-inch masonry bit in a hammer drill. Drill a hole on the soapstone line that goes completely though the brick. Drill one hole every 1/4-inch until the entire vent outline has holes. Align the tip of a cold chisel with two of the 3/16-inch holes. Strike the chisel with a 20 ounce hammer.
Chisel along the drilled holes until all holes are connected by a light score line. Strike the area in the center of the score repeatedly with the hammer until it breaks out of the wall. Remove jagged edges from the brick remaining inside the hole with the chisel and hammer.
Press the vent cover against the brick wall with the center opening sitting inside the hole. Set a 2-foot level on the cover's top flange. Adjust the cover until level. Push a pencil into one of the vent's mounting holes. Move the pencil in a circle to mark the location on the face of the wall. Mark each mounting hole as described while ensuring the cover remains level. Set the cover aside.
Drill a 2-inch-deep hole at each pencil marked mounting location with the 3/16-inch drill bit. Push a plastic masonry anchor into each hole. Tap the anchors with a hammer until they sit flush with the surface of the brick.
Slide the pipe section of the fan over the back opening of the vent cover. Apply a bead of silicone -- use a squeeze tube to reduce waste -- to the back of the vent cover. Press the cover against the brick wall. Thread one screw into each plastic masonry anchor by turning them clockwise with a Phillips screwdriver.
Mount the fan section of the fan vent to the inside of the brick wall using the same method used to secure the vent cover to the outside of the wall.
Hire a certified electrician to wire the fan motor. Most building codes will not allow a homeowner to run electrical wiring.