Buy a rack that's made to fit your bike's wheel and frame size. If your bicycle frame has mounting eyelets on the seat stays, the diagonal frame members on the rear of the bike, choose a rack that bolts to them. If not, buy one with a universal mount that attaches to the seat post or the brake bridge, or clamps over the stays.
Bolt the rear supports to the dropouts using the hardware provided with the rack. Leave the bolts loose so the rack can swivel at the attachment point.
Attach the front brackets to the rack, leaving the fittings loose. If the brackets attach to eyelets on the seat stays, screw the bolts into the eyelets. Level the rack and finish tightening the bracket bolts.
Remove the rear brake fixing nut if your front bracket mounts on the brake bolt. Slide the bracket through the brake bolt from behind and re-install the nut, making sure the brake shoes are centered with respect to the rim.
Attach the clamp assembly around the seat stays if the bracket mounts there. Make sure the rack is level and tighten the screws.
Install seat post mounted brackets by fitting both sides of the clamp around the seat post, leveling the rack and tightening the bolts.
Finish tightening the bolts that secure the rear supports to the dropouts and mount the reflector bracket and reflector according to the manufacturer's directions. Re-tighten all the mounting screws and bolts after riding 50 miles.