Through the overdrive website your library had, you should have the option to check out ebooks for the fire. You use your library card number to access them, and then put them in a cart. They are delivered, so to speak, via amazon. It was very easy to do. Good luck! I have enjoyed getting books this way.
Yes, very easy! Simply click the Overdrive link your library's website. After you add books to your basket you click the checkout button and continue following the directions. You're eventually taken to the Amazon site where you have to have an account set up to have the books delivered.
With Overdrive you can also be put on the waiting list for a book and you'll receive an emial notification when it's ready for you to check out.