I have posted few donate books Ads for donating my books, what happens next ?
Now, you can wait till a book requestor contacts you and then you, pass over / handover the book to him/her or to organization (who ever approaches you)
To expedite FASTER - you can directly check the "Requested books List" means which all books are already asked/ requested by different user and then check if any of your books which you want to donate matches with what is requested by other users. Call on their phone number and pass on your books to him/her.
To speed up your donation FASTER, you can also try sharing the link/url of your book donation Ads in social media like Facebook and Twitter etc.