I put my thumb slightly behind the middle on the bottom and put a little pressure on the back of the bun with my pinkie fingers so that the stuff inside has a gentle pressure towards my mouth. While some sauces might escape, the toppings and meat stay in.

Usually I see people blow out their burgers by holding the part closest to their mouth in a counter productive attempt to squish it into their mouth.

Edit: oh neat, the image posted by ThatWeirdGuy is exactly what I’m talking about!