We will first cover the iPad, then cover the Barnes and Noble nook and lastly cover how to use Calibre to put it on other devices.
If you are using a kindle check out this instructable: http://www.instructables.com/id/Converting-EPub-Formatted-Books-to-Use-on-the-Kind/
Step 1: Install The iBook App on your iPad
Once it's downloaded and installed we can start putting books on the iPad
Step 2: Obtain the E-Book
Put the ebook somewhere you can get to easily, like the desktop or in a folder called "Instructables Ebooks"
Step 3: Update iTunes
Once you have the newest version you can continue.
Step 4: Drag File To Your Library
You can also do this by going to: File > Add to Library and navigating to the ePub file.
Step 5: Connect Your iPad And Sync Books
if the iPad is synced with the computer, connect the iPad, go to the Books tab of the iPad (not books under the "Devices") and sync the appropriate EPUBs that will show up as Books
if the iPad is not synced with the computer, check the "Manually mange music and videos" checkbox in the iPad's Summary, and then drag the EPUBs from the iTunes, Library, Books section to the iPad.