You are pulling the puddle if the electrode is tilted toward the direction of travel. When pulling, the electrode is pointed back toward the bead that is being laid down.
You are pushing the puddle if the electrode is tilted away from the direction of travel. When pushing, the electrode is pointed forwards, toward the joint that has not yet been welded.
Whether to push or pull depends mainly on what welding process you're using. As I understand it, stick is almost always pulled, whereas TIG is usually pushed. I don't know about MIG. The reason stick is pulled (again, as I understand it) is that you want the arc force to be pushing the slag back away from the puddle. With gas-shielded processes, this is unnecessary, since there isn't any slag.
The angle that should be used is independent of what hand is holding the gun. When pulling, it is usually easiest for left-handed people to go right-to-left, and vice versa for right-handed people. When pushing, it's opposite. The reason is that these configurations keep your hand and arm out of the sight-line to the puddle. Going the other way tends to put the hand, gun, or electrode in the way of the puddle, making it harder to see what's going on. Of course, a skilled weldor should be able to work around this, because there are always going to be some situations where you have to move with the puddle partially obscured.
EDIT TO ADD: I think another reason people tend to work a certain direction depending on their handedness is that it's always easier to work "inside" your body vs. "across" your body. This is the same reason a forehand shot is easier in tennis than a backhand shot: because with a backhand, you're reaching across your own body. The same is true if you are left-handed, and are working left-to-right with a pull technique. The degree to which you're crossing your own body is less than with a backhand, but still, your left arm is extended towards your center-line, and then your wrist is cocked to hold the gun to the left, while pulling the bead from left to right. You're crossing your own center-line and then back again. Your elbow gets in tight to your body and you lose flexibility.