Make it easy to donate and price appropriately.
I have an online second hand book business and I buy large quantities of books at auction. I keep probably a third for my own use or to sell on. The rest, provided that they are good quality, I am happy to donate to charity - paperback novels, children's books, glossy reference books.
Where I used to live there was a specialist Oxfam Bookshop in the city centre which had collecting bins in supermarket car parks all over the city. You just pull up alongside, put your books in the chute and away you go.
Where I live now, there is an Oxfam Bookshop in the town centre but no collecting bins, nowhere to park nearby, no delivery yard. Clearly I am no going to lug three large boxes of books from the nearest car park, so they are losing out on large quantities of free stock.
I would agree about displaying books alphabetically and also non fiction by category. It's really important that children's books are properly sorted and preferably arranged by author.
Look at ways of keeping stock turning over - bargain rails of clothes for £1, rummage boxes of little toys for 20p, fill a bag of books for £5.
If you aren't able to check that games and jigsaws are complete, don't charge a lot for them. People will pay 50p for a jigsaw, take it home and do it and if pieces are missing, well it's only 50p. They won't want to do it, if you are charging £3-£4.
Nothing is more off-putting than a charity shop where the stock has been there for years