Copy-editing is the second stage of editing for publication, and takes place after any structural issues have been rectified by the author. The role of the copy-editor is to carry out an in-depth check of the text before the document is typeset to produce a proof copy (a trial print of the finished book). This includes checking for continuity problems, loose ends, minor plot holes, inconsistencies, and spelling, punctuation, and grammatical errors.
At the copy-editing stage, I work with the electronic version of the typescript (usually a Microsoft Word document) making any changes onscreen. I use the Track Changes feature to mark up the text: to add comments and queries, to insert or delete text, and to make any formatting changes. Some minor rewriting may be required by the author at this stage. Some clients prefer to work with them on a chapter by chapter basis; others prefer me to work through the whole document first. Personally, I prefer the former as it provides continuity with the client, and enables me to further development their writing skills as we progress though their work.