What kind of new tablet do you use? If it's an iPad, you are able to download books to iPad directly. Just launch iTunes on your tablet and go to iTunes Store, then search for the book you need and click Get below the book cover.
When you want to download ebooks to iPad, you are able to sync the books with iTunes. Having the latest version of iTunes installed on computer, you are able to connect your iPad to computer with USB and sync ebooks to computer.
After getting the ebooks in iTunes library, you are able to sync the books to iPad easily. The following guidance will show you how to finish the task.
1. Plug iPad into computer via USB, and iTunes will launch automatically.
2. Click the iPad icon and choose Books category in the left sidebar.
3. Check Sync Books and choose All Books or Selected Books.
4. Click Sync at the right bottom to start syncing books to iPad.
After syncing books to iPad with iTunes, you will get the books in the iBooks app on iPad. Now you have an enjoyment. But note that you should shut down auto sync before you sync books with iTunes. To shut down auto sync of iTunes, you need to go to Edit > Preferences > Devices on iPad, and check "Prevent iPods, iPhones and iPads from syncing automatically".
If you have downloaded or got books from elsewhere, you can add books to iTunes at first, and then sync these ebooks to iPad. To add ebooks from computer to iTunes library, you only need to click File > Add File to Library at the upper left corner of iTunes, and then the ebooks will be added to iTunes Book Library.
Visit this guide for more methods about how to transfer books to iPad tablet. http://www.leawo.org/tutorial/download-ebooks-to-ipad.html