How do landing fees work at larger airports?
Well, the short version is that there really isn't a standard (and this applies to small as well as large airports).


Some airport authorities charge fees that are billed through the FBO, some don't.
Some airport authorities bill you directly, some don't.
Normally you pay at the FBO before you leave.  
Most of the FBO's set their own fees (although they may come from corporate).
Some FBO's don't charge any fees (although not very many these days).
Some FBO's waive some (or all) of their fees if you buy fuel, some don't.
Most FBO's charge a fee based on the size/class/weight of aircraft, some don't.


In short, call ahead to the FBO that you will be using and ask them what the fees are and whether or not any of them can be waived.  They are used to this question and will have the information handy for you.