In creative writing, it is much more important to get your ideas onto the page than to proofread as you write or after your first draft. For example, in the past, with major publishing companies, an author would first be assigned a developmental editor, then a general editor, and finally a proofreader. I am not sure if this process is the same today, but I do know that many of the best writers hire their own personal developmental editors.
Developmental editors help shape the big picture of a book. They assist with structure and organization, character development, and making sure sections appear in the most effective chapters. They may cut sections or even entire chapters that do not fit the book. In addition, developmental editors may ask the author to write new chapters. A first draft rarely has chapters in the best possible order. Many celebrities seek excellent developmental editors to help start and organize their books. Very few editors have the skills of a great developmental editor.
After the developmental editor completes major structural work, the general editor focuses on details within chapters. This includes paragraph structure, word choice, transitions between chapters and paragraphs, possible anachronisms, timeline mistakes, and more. Book editors also watch for continuity errors, awkward phrasing, and unclear ideas. There is not a hard line between a developmental editor and a general editor.
A proofreader reviews the manuscript to correct small mistakes before publishing. They focus on spelling, grammar, punctuation, capitalization, and formatting. Proofreaders also check for consistency, such as correct use of names, dates, and headings. Unlike editors, proofreaders do not change ideas or structure. Their role is to ensure the final version is clear, polished, and professional. If proofreaders find major errors, which happens often, they alert the author. The author then sends the manuscript back to the editors, and they plan how to fix the mistakes.
To answer your original question about the best way to proofread, you should first learn sentence structure skills and then paragraph structure skills. At this level, an instructor teaches you much of what editors and proofreaders do and gives you the tools needed to proofread effectively. If you learn the skills as you learn to write, you will feel the power of the written word.