There are all sorts of personalities out there that do freelance editing. There are those who need to bill to pay the bills. Others may be willing to gamble on a percent of royalties like an agent. I have accepted a percent of royalties as a payment form but I'm not sure if others would.
A freelance editor is somewhat like an agent. I like to get a preview, usually the first chapter and a middle chapter and a back cover blurb, to determine how much effort will be expended to complete the process. I may reject a novel and recommend a writer's site, schooling, or writing books for works that don't meet a certain level of competence. I may reject a novel if I think it doesn't need any further editing and recommend they start peddling it to agents. In some cases, where the story has merit but the writing needs a lot of work, I will offer to work for a flat fee, no matter how long it takes.
As a writer, you also need to find a good fit with an editor, so don't pay very much up front. Make a contract that allows either party to withdraw from the enterprise after a certain number of interactions (I recommend three sets of three chapters (could be the first three chapters three times) - around $200 or less). By that point in time, both parties should know the fit - if it fits like a glove, be suspicious, if there are agreements and disagreements, be pleased, if there are only disagreements, run. By then, the editor should be willing to give you a firm quote to complete the task.
Always remember - it is your novel and you have final say but dismissing an editors suggestions without due consideration is questionable. In other words, even if you disagree with a suggestion, file it and review that file more than once. You never know when something that sounds wrong today may become correct tomorrow.
Cautions - billing can increase significantly if there are copious notes or could be less if there are few notes. If the first chapter is filled with notes and comments and the editor continues with the next two chapters, you might be getting ripped off. In my opinion, if a lot of work is need in the first chapter, then a new agreement or a termination of effort is proper. Fees vary from $600 for a 120,000 word novel to $6,000 and more and that's a lot of cash so be wary of those asking for a excessive fees, they may be worth it but are there others out there that can provide the same quality for a lot less?
A long answer for a short question. Sorry.
Smiles
Bob