Downloading library ebooks to a Kindle is a simple process and this post will get you started. Before going further though, please note that the Kindle Fire works like an Android tablet and the instructions for downloading to a tablet can be found here. For all other Kindles: the Paperwhite, the Kindle, and the Kindle Keyboard, here's the scoop...
Downloading to a Kindle requires that you start the process of searching for and checking out an ebook by visiting our Overdrive collection on your computer. Once you find an ebook, select the Kindle format version, login with your library card, check it out, and click the "Get For Kindle' link. You will be taken to Amazon to complete the free transaction. Amazon will give you the option of delivering the ebook to your Kindle via Wi-Fi or by downloading it to your computer where you can plug your Kindle in with the USB cable and drag and drop the ebook into your reader. Some publishers restrict whether or not their Kindle books can be delivered via Wi-Fi or must be transferred via USB.
For more help, see these two videos that walk you through the process of downloading to a Kindle.