How should I go about selling a large number of unsorted LEGO sets?
You have three basic choices, depending on how much time you want to spend:


Sell the collection as-is (with as much honest description as you can muster and great photos if you're selling on-line).
Sort the collection into sets and sell them as-is with parts / figs missing.
Sort into sets and replace missing parts / figs.


These three are not mutually exclusive.

Personally, I'd go with the first option unless you have a lot of time on your hands and are a real enthusiast. Otherwise, your time is probably worth more than any additional profits you might make. At the same time, there are plenty of us who would love to take on a collection like this.