As requested by "keke_eo" over at LingQ, here is a picture of how I lay things out.
Simply slide the covering books slowly downward as you read and you'll be able to easily keep your place, keep the books open and have the freedom to take your hands away at any time. I recommend you do this at a high table as this will save you from having to bend your back too much.
I also have a tip for preventing damage to your books. Assuming you are reading a language in which you read from left to right, when you begin a book you should start off with the left half of the open book being very thin and the right half being very thick, or vice versa for a language like Japanese.
This means that the weight of the covering book is pretty much entirely being supported by one half of the book which you intend to read. If you put another similar sized "support book" under the thin half of the book you are reading, the weight of the covering book is evenly distributed and puts less strain at the point where the page joins the spine. (If you look at the book on the right of the picture, you will see the red "support book" sticking out a little.)
Doing this will help prevent the pages from coming away from the spine. By the time you are midway into reading your book however, you don't have to do this anymore. When the other half of your book starts to become quite thin though, place a book under what has now become the thin half to again reduce pressure at the spine.
Anyway, I'll be updating again soon within the next couple of days about my progress in reading this Harry Potter book.