How to correct errors in proofs of an accepted paper
Here is my method of correcting proofs.  I write my corrections in a text document.  You can also use the review mode of a PDF viewer.


The copyeditor provides a numbered list of questions.  I respond with a numbered list of answers, with one answer for each question.
If there are repeated errors, I list those first.
I give a numbered list of corrections.  These go from the start of the paper systematically to the end.  Each correction begins with the location, including page and line or figure number.  Each correction quotes the error and correction explicitly.
If figures need to be replaced (which does not happen in practice) then I prepare those as separate files.
I verify author names, affiliations, and grant numbers in acknowledgments.  
I ask the copyeditor to send me a second proof, if the corrections are significant.
Everything is submitted according to the instructions, which are different for each copyediting company.  Usually there is a web form.