How should I list a past employer that is no longer exisiting on a resume?

Just list them as a past employer as you would any other, and put, perhaps in parenthesis, that they no longer exist.

The fact they no longer exist is only relevant if you are short of people to ask for references. If you have another good recent reference, fine. If this employer is the only one you've had in recent years, then you're a bit stuck and you will have to explain in the references section of the resume that they no longer exist. Is your boss there contactable some other way? Of course if the company went bust in suspicious circumstances then you might not want a reference from them anyway.

List as "previous employer name, location (dissolved/no longer trading)"