Near the start of the game, you'll follow the psychopomp Sam to a bar called the Schoolyard Strangler. Once there, you'll need to sneak into a party, upstairs. You are given the option to distract the bouncer by instigating a conflict, or earning yourself an invitation by beating a demon at blood pong. Obviously, choose the blood pong.
Playing as Lola, you need to sink a ball in three cups in just three throws. Using the background to line up your shot, aim the shot across Milo's hair to hit the first cup. There is also an angular rock in the wall, directly above Milo's head. Aim about 1/3 of the way up to that rock, from his head, to hit the second cup, and 2/3 up to hit the third cup. (This guide is to be used with the default throw power. Please see Update 2 for clarification.)
Luck plays a factor. So does hellcohol. The more you drink, the harder it is to aim. If you are drinking for the dialogue options, and your opponent is sinking his shots, it will become impossible to land your third shot, so bear that in mind.
If you miss a shot, immediately quit to the main menu, and then load up the game again. Unfortunately, you will have to sit through a bunch of dialogue again, to get to the minigame.
Update: "Its Dan" provides a helpful tip on skipping some of the dialogue, in the comment section, below.
Update 2: "Stevivor" points out that you can also change the power of your throw, by moving the stick left and right. As I was unaware of this feature, my aiming guide is to be used with the default throw power.