My shelves are screwed to the wall and cannot be adjusted, so my books are organized mostly by size.

Topic and then by author -- I have over 4000 books. When I need to refer to one, I know the topic but not always the author. So, this makes more sense for me.

I organize my library by topic. Animals, Art, Biography, Business, Economics, etc. Within each category, I have sub-categories. I use the on-line Libib.com library management software. I can access my book titles from anywhere in the world. I also use it for my video library.

Good question. I'm in similar quandary, hoping to organise about 500 poetry books ranging in specific names from Chaucer, to McGough via Service, Patterson, Lawson, Lorca and Naruda to anthologies general and specific.
Perhaps I should make separate post.

Non-fiction by subject and fiction by author within genre! And then rearrange from time to time. Did American History by event date for awhile.

When I had a library ( left everything when I moved) it was organized by Author then subject. I only have 5 books now on the floor.

I organize books by topic first. This shelf for language reference books, this shelf for nonfiction, this shelf for fiction. Within each shelf, I organize loosely by size, tending to put the taller/wider books toward the outside. I organize by series, like all the Game of Thrones-related books in one section of a shelf. I organize by topic, like all the books about Benjamin Franklin grouped together, or wildflower field guides vs. gardening references. Books only get organized by author incidentally to the topical organization. I just noticed that I pay no attention to alphabetical order at all. My collection of books isn't that large, and I know where the topical sections are. I can usually retrieve a book in fairly short order, and when that fails, it usually turns out the book is in the wrong place. (Looking at the nearest shelves now, I have a French book in the garden reference section for some reason. Probably because my language shelf is packed absolutely full.) Anyway, it's an imperfect system, but it usually works.

I orginize by genre.

Total chaos, it sometimes takes ages to find one when I want it but I always tell myself that I enjoy the challenge.

I organize my books according to the main categories of the Dewey Decimal System. This helps me to easily find books on my bookshelves, and to avoid buying second copies of books I already own.

By author for older books. By purchase date for the To Be Read shelf.

I have mostly fiction books and I organize them by author. Non-fiction books are in their own section by 'movies', 'history', etc.

Vaguely by category and size.

Genre. Fantasy, sci-fi, horror, and the overlapping ones in between.

I got so many books that I have to put some of them into boxes. No organization what so ever there. There is no more room in my house for more books so they boxes are stored under the house and I take them out as I have red what I have inside the house. As I constantly buy more books it's taking a long time. I tell myself one day when I retire I will have more time to read.