The Club Key in Resident Evil 2 is a large silver key, and it is one of the four "card themed" keys you will need to find in order to progress trough the main game.
The first step in getting the Club Key is to find Ben in the cells of the Police Department. He will ask you to head to the kennel to access the sewers, to head that way. Remember to grab the crowbar next to him first tough. When you find the manhole that leads you to the sewers, go in and make your way trough thit. At one point you will reach a locked door near the Septic Pool, but boost Ada through the vent and take control of her.
After entering this room, follow the little girl that runs away from Ada until you reach the Cesspool Tank. Kill all the zombies here, and drop down until you find a box, shortly followed by two more boxes. Line these up to a straight line and head back where you entered the room. Press the control panel with the green button, and this will flood the room. Now use the boxes you lined up to walk across the flooded room and grab the Club Key!