Q. How do I get books from the library onto my Kindle?
You will check out the library books from the library's OverDrive website.
OverDrive will give you a temporary license to read a book, but it has to be one that Amazon has in the Kindle format. When OverDrive connects to Amazon, it's like OverDrive says "Hey, this Kindle user of yours can use this book for three weeks." Amazon sends the book to your Kindle, with an expiration date on your permission to read it.
You do not need the OverDrive app or the Libby app, although you may choose to use them.
Here's a help article with screenshots to show how it works.