Use a screwdriver to remove the housings and casings on the trimmer so you have unfettered access to the engine.
Disconnect the coil module from the spark plug boot by pulling the connection off with needle-nose pliers. Disconnect the ignition wires from the coil module to the engine in similar fashion.
Unscrew the remaining fasteners holding the module to the engine. Pull the coil off the weed eater.
Pull both the spark plug boot and the spark plug coil spring off the old module for transfer to the new one, since these components typically don't go bad. The spring has two sharp ends that puncture the spark plug wire; they'll require removal. Pulling at them gently is enough to dislodge them.
Slide the ignition wire heat shield off the old module and use needle-nose pliers to pull out the ignition wire. Place each of these pieces on the new unit, in reverse order from how your removed them. The heat shield slides on over the module wires first, followed by spark plug coil spring and the spark plug boot. The ends of the coil spring push through the insulation of the spark plug wire. Use the pliers to accomplish this. The coil sits on the end of the spark plug wire once it is connected.
Attach the new module to the weed eater engine in the same fashion that you removed the old one. Screw the fasteners back on but don't tighten them yet.
Rotate the flywheel so the magnets are facing the ignition module. Place a spacer card or a thick business card down on the magnet, then tighten the fasteners back on the module. This maintains the proper distance between the magnets and the ignition coil. This is important for proper function.
Reconnect the spark plug boot and ignition wires. Pull the card out once the module is secured.
Screw the casings and housings back on.