Instructions
Defeat Whitney in the Goldenrod City Gym to get the Plain Badge. Head north and follow the path to reach the National Park.
Register to enter the bug catching contest at one of the gatehouses on Tuesday, Thursday or Saturday. Walk around in the grass until a Scyther appears. Reenter the contest until you find a Scyther.
Weaken Scyther in battle and use Park Balls until Scyther is caught. Retire from the contest, and Scyther will be added to your roster or sent to your PC box.