As with everything in the pipe, it's best to suss out how much pop you need to get off the lip. To do this, have a bit of a practice with straight airs to get a feel for it.
The Alley Oop is a spin against the direction of travel, so it might not feel completely natural. To initiate the trick, it's all about being subtle and smooth, so don't be jerking yourself around! As you ride up the wall, put your weight onto your uphill ski. When you're at the top of the lip, twist your torso and look towards your uphill shoulder, this should naturally initiate your rotation. You need to spot your landing on the floor of the pipe. You'll want to try and stay as compact as you can throughout the rotation.
Once you've begun your spin, try and put a grab in, like Josh has done above. Aim to hold this grab thought the whole rotation. If you can do this, not only will it look pretty sick, but it also helps to keep you balanced and controlled.