How is one supposed to properly eat multi-level hamburgers?
The trick to eating a large hamburger the size of a McDonald's Big Mac (or even a Double Big Mac with four patties) is to grip the burger firmly while crushing it down a bit. It may take a big of practice to get right, but it's something most eaters of hamburgers seem to do instinctively. So much so I can't really describe the technique in a lot of detail, but the basic idea is you're both making the burger somewhat smaller and holding it together firmly. You want to grab it in both hands with your thumbs underneath. Your fingers should be spread out over the top, compressing it down, while your thumbs pin everything in place.

If you watch pretty much anyone eat a hamburger, even normal sized ones, this is how they'll eat it. There's really nothing special in how you need to hold it, the trick is applying the right amount of pressure. Bigger burgers will need a more firm grip, while normal sized burgers can be held fairly loosely (though you'll still see people crushing them anyways). There's a limit to how big of a burger you can eat this way though. It should work with pretty much any burger normally sold by the big fast food chains like McDonald's or Burger King. There are however restaurants that sell enormous burgers that can't really be eaten in any sort of normal way unless you have really big hands.

I should also point out that you sometimes do have the option of going wider rather than taller with hamburgers. For example the Big Mac has two 1.6 oz (45.4 g) patties, while the Quarter Pounder with a single 4.25 oz (120.5 g) patty is both bigger and easier to eat.