Complete the most self-editing possible beforehand. This applies to every type of editing. The better foundation you give your editor, the more she can help you. If she’s fixing basic writing flaws you could have improved with self-education or another pass before your sent it, she’s spending less time strengthening your MS in other ways. Some more sophisticated work simply can't be done if the foundation isn't strong. Example: In a line edit, your copy editor may spend a lot of time cutting out hedge words that pad writing without adding anything. If a scene first needs to be trimmed of clichés and unnecessary words, it's harder to drill down into word choices that can make a big impact on tension or emotional impact. Your editor will help you with these things if you need it! But a polished book, no matter what, takes many rounds of editing. If you are not self-editing before you hit send, you're not getting the most bang for your buck.
Always ask for a sample edit. This helps you know what you’re getting, whether you're a first-time novelist or an experienced one who knows what they want from an editor. Not every editor is right for your book or your personality--this has nothing to do with the editor's skill and everything to do with their style. I once saw a markup by an editor that was downright insulting. It worked for the author, who apparently had thick skin, but for most of us, a kinder touch is appreciated!
Ask for what you want. If you have specific concerns or questions, absolutely mention it to your editor! As with every relationship, communication is key. This could be a big issues, such as: My participles dangle. Please fix these in line. Or small: American spellings all around, except for the word "grey." I just like it better that way.
Remember that your editor’s changes are always only suggestions, but that you are paying for her/his expertise. An editor will have a reason for their edits and suggestions. If you're not sure, ask--an author knows what they meant, and may have trouble seeing, for example, ambiguity that might trip up readers.