Instructions
Complete the main quest line by defeating the Elite Four and gaining the National Dex.
Go to Route 12, which is south of Lavender Town and north of Route 13.
Visit the house in the middle of the route, and speak with the man inside. He'll give you the Super Rod.
Turn on your radio, and select the channel in the top-right corner, Professor Oak's Pokemon Talk. This is a talk show that discusses Pokemon affairs, including when certain breeds start swarming. There is a slight chance that he'll mention a Luvdisc swarm on Route 27. If he doesn't, check back the next day.
Travel to Route 27 if the Luvdisc are swarming. Route 27 is east of New Bark Town and west of Route 26.
Stand on a dock or pier, and use the Super Rod. You'll reel back a random fish. There's a 50 percent chance that the fish is a Luvdisc.
Fight the Luvdisc until its health meter is yellow or red.
Throw a Pokeball at the Luvdisc when it's weak. If you miss, throw more Pokeballs until you catch it.