Unplug the Dyson, and turn the appliance upside-down on a flat surface.
Twist the three screws in the soleplate, which is the cover plate on the bottom of the vacuum, counterclockwise to release and remove the soleplate.
Slip the drive belt off the left side of the roller brush using the end of a screwdriver. Take care not to nick or cut the belt.
Pull off the corrugated hose on the brush holder, and unscrew the other end of the hose from the upright section of the vacuum.
Pull the brush holder back and forth with gentle pressure to pop it off the Dyson.
Use a screwdriver to remove the three screws holding the clutch plate over the motor cover. Take off the clutch plate.
Turn the Dyson on its side, and use a flat-blade screwdriver to pry off the clip holding the motor ball on one side. Turn over the vacuum, and remove the clip on the other side.
Pull the ball downward, away from the upright portion of the vacuum, to disengage the part.
Pry apart the two halves of the ball to remove the motor.
Disconnect the two wires on the motor from the Dyson wiring harness by unscrewing the wire connectors. For future reference, the red wire motor connects to the brown wire on the harness. The black motor wire connects to the blue wire on the harness.