This must be done in a Ranked Match.
While running around the areas of Rapture you will see an announcement at the bottom of the screen. "A Big Daddy suit has spawned near your location", make your way to the suit if you know where it is and press to wear it.
Normally this turns into a mad scramble between players to get the suit. If you do see the suit laying on the ground grab it before someone else does.
You can use any game mode other than Capture the Sister as players will spawn as the Big Daddy.