It's not that simple here - no dishwasher.
Heres what I do:
1. Fill up sink with book out of way so it doesnt get wet.
2. I prop the book up to the right of the faucets, opened to the correct page & put the bottom left corner of the book behind the sprayer thing.
3. I keep the pages open with a clothespin on the top edges of each side.
Of course, you have to dry your hands to turn the page, and it doesn't work wellwith very small books. You also have to pay some attention to the dishes. I generally cant rinse and read at the same time! I came up with this because I had borrowed a few books on tape from my neighbor, but I had to keep stopping, drying hands and rewinding. I cant seem to concentrate on someone reading to me.
I hope this helps. I do like the dishwasher idea phil_t- maybe someday