Instructions
Go to Pastoria City, which is to the southeast of Hearthome City and is accessible via Route 212. If you have a Pokemon with the Fly HM, simply fly there.
Go to the Great Marsh. The entrance to this area is just northeast of the Pokemon Center in the northern half of the town. Go into the building and head up the stairs. Use the binoculars to look out into the Great Marsh; this will tell you if Croagunk is there that day and, if he is, where you can find him. If he does not appear, check again the next day.
Go downstairs and speak with the woman at the counter. There are two women here; speak to the one closest to the back door. Pay the 500 Pokedollars to be allowed to play the Safari Game. Go through the door near the counter to reach the Safari Zone.
Explore the Safari Zone. Use the trolley system to travel to the zone where you saw the Croagunk. Walk around in the grass until you encounter one. Croagunk is extremely rare, so you may need to pay to play the game a few times before you catch one.