You can download free and paid books from Apple's iTunes store and read them on your iPad with iOS 7 using the free iBooks app. Apple allows you to download books from other sources as long as they are not copyright-protected and are in ePub or PDF formats, so you aren't restricted to using iTunes to build your library.
Download the iBooks App
Tap the App Store icon on your iPad's home screen. Type "ibooks" in the search bar at the top of the screen. Select iBooks from the list of results that appears as you type or tap "Search" on your keyboard when you're done typing. In the iBooks preview, tap the "Free" button, tap "Install" and enter your iTunes password if prompted. Wait for the app to download and install; you're good to go when the button changes text and says "Open."
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Finding Books to Download to Your iPad
Tap the iBooks icon on your home screen to open the app. To browse for books to download, tap "Store" at the top of the screen to go to the iTunes book store. On the main page, you'll see recommended or popular books -- look at the top of the screen to find genres and the bottom to find further categories. If you know what you're looking for, go to the search bar and type in the book's name, author or a keyword. If you see what you're looking for as you type, select it. Otherwise, finish typing and tap the "Search" button on your keyboard.
Downloading a Book on Your iPad
You can download a book directly from your search results or, if you want to read more about the book first, tap the associated preview to open the description window. To download a book after you have located what you want in the store, tap the button displaying the book's price. The button should then change to "Buy Book." Tap the button, sign into your account if prompted and the book will download. To check that your books have downloaded to your iPad, tap the "Library" button at the top right of the screen to return to the iBooks app. Tap the book to open it.
Tips on Downloading Books From iTunes
Samples are available for most books in the iTunes store; find the book you're looking for and tap the "Sample" button to download a preview of the book. If you're interested in free books, look for the "Free Books" link in the Quick Links area of the iTunes store's main page.
Downloading Books From Other Sources
You can download books onto your iPad from other websites or from your computer. These books should in the ePub format and free of digital rights management, free. Apple recommends that you download external books via iTunes on a computer by adding them to your library, but you can do this from your iPad in some cases. For example, if you are browsing a site in Safari on your iPad and want to download a book with an ePub link, tapping the link should give you the option of opening the book in iBooks. This also works if you copy ePub links and email them to yourself. There are other apps available in the App Store for reading books associated with other e-reader accounts, including apps for the Amazon Kindle and the Barnes & Noble Nook.