Instructions
Head to Pastoria City via Route 212 going southeast from Hearthome City. Make the trip quicker by using a Pokemon with the Fly HM ability to fly you there.
Navigate to the Great Marsh, which is northeast of the Pokemon Center in the northern part of the town. Enter the building and head upstairs. Walk up to the window and use your binoculars to examine the Great Marsh. Keep a look out for Croagunk; if you don't see him you'll need to come back another day. If you see him, you'll know where to go look for him.
Head down the stairs and talk with the woman standing behind the counter. She will ask you for the 500 Pokedollars it costs to play the Safari Game. Give her the money. She will direct you through the door near the counter.
Go through the door into the Safari Zone. Use the trolley system near the door to head directly to the area where you saw Croagunk. Walk around until you find him. Use Psychic and Ground attacks to weaken him during battle and then throw Poke balls until you capture him.