To replace a flyback is straightforward. Discharge the picture tube, undo the rubber suction cup (anode connection) from the tube. Unsolder the focus voltage (8,000 volts!) wire from the picture tube socket on the neckboard. Unplug the screen voltage (600 volts!) single pin connector from the neckboard. Now remove the monitor main board and flip it over. Unsolder all the pins of the flyback from the foil side of the circuit board.
Flybacks can be quite expensive depending on the make/model of monitor. Some flybacks are around $25 while others can go as high as $150 each.