Briefly, you need the latest version of InDesign CS6/CC, a copy of Adobe Digital Editions (free from Adobe) to check your ePub. You'll probably need to fine tune the HTML/CSS so an application to zip/unzip the ePub file and an application such as BBEdit, Dreamweaver or Oxygen Author to adjust it would be good. If you want to produce Kindle editions (recommended), you'll need a converting program from Amazon (free), and finally a device or two to check the output.
Just my thoughts!
In addition to Derek's comments, it is always a good idea to check your ePub for any errors with this free application: http://validator.idpf.org/. If you are using the printed version as a base for your ePub, you'll probably need to tweak it a bit before you export to ePub.
Yes, you're right - the validator is vital too!
It's also highly recommend that you read a good source on how to prepare your InDesign files. It's not as easy and intuitive as creating a PDF. It requires some specific preparation style for applying styles, tagging styles, choosing a method of defining export order (e.g., the Article panel), preparing a TOC style, learning how to create page breaks, etc.
The two best sources for this information are NOT from Adobe, are not in the Help file. They are:
(1) Videos by Anne-Marie Concepcion on Lynda.com. She has prepared videos for CS5, CS5.5, CS6 and is currently working on a version for InDesign CC. If Bob Levine sees this post, he has a link to a free week trial for Lynda.com.
(2) eBooks by Elizabeth Castro at www.elizabethcastro.com/epub/.