It's done by twisting the lower torso. For a right hander, being able to shift/twist the right hip away from the cue.
For the standard player this takes a lot of stretching and pain in the back leg hamstring and torso and neck muscles. Hard to pick up as an older new player, but can be done.
Else, you end up with the shoulder right of the cue line and a chicken wing elbow to make a semi-straight shooting action.
edit: The quick fix is placing your feet more in line with the shot, though the best cueists still stand nearly square on and have great lower torso flexibility... watch the snooker players to see this. eg Ronnie O'Sullivan, Stephen Hendry.
ChopStick:
The advice you've received thus far seems to be dead-on -- especially Colin's concerning how the snooker players do it. Proper snooker fundamentals are all about proper alignment (every body part), and the shoulders are no exception.
Perhaps you should try pointing your feet directly into the shot -- I mean both feet, not just your left foot if you're a righthander, or your right foot if you're a lefthander.
As an example, if you're a righthander, draw the shot line out from behind the cue ball onto the floor, step directly onto it with your right foot -- keeping your toes pointed into the shot line, keep that right leg straight (no bend in the knee), and then bend / fold your body over (from the waist) onto the shot line.
In other words, with your right leg straight and that right foot stepping onto and pointed into / parallel with the shot line, "flop" your upper body over as if there were a hinge at your waist. While doing so, keep your shoulders square, reach over from your left and place your bridge hand onto the shot line behind the cue ball. You'll want a 60/40 or even 70/30 weight ratio between your left and right legs (with the most weight placed on the foot that is on the shot line -- the right foot in this case).
It will take a bit of practice, but you'll get where you should be standing in order for your left hand (bridge hand) to fall properly behind the cue ball at the proper bridge length.
When you get it right, you'll find that your shoulder pretty much automatically falls behind your head without even thinking about it.
The alignment of the feet and legs have a TON to do with how the upper body is aligned.
-Sean