If you don't have a library card already, I recommend you get one. Check with your local library on the requirements to get a library card as well as what their virtual library offerings entail. A library card can give you access to potentially millions of e-books to download on your Kindle or another e-reader or tablet.
Once you have a library card, you can log into your library's website with your credentials, then search through the site to see what platform it uses for its virtual catalog. OverDrive is a platform used by many public libraries in the US that features millions of e-books and audiobooks and is available through participating library websites.
If your library uses OverDrive, then the app to download on your mobile device is Libby. With this service, you can browse through the virtual library and borrow books to checkout for free.
Hoopla is another service affiliated with many local libraries across the US, but their content catalog features much more than e-books: you can find movies, TV shows, magazines and music.