They say you don't need to print anything, 99.9% of people have no problem but I have read 2 or 3 threads recently where the system has not found the ESTA's. I would always print off if possible but at least take the ref numbers.
I just print the front page with the confirmation number on it. If you hit print and let it churn out the pages on its own you end up with several. As Wayne says, if you have a confirmation number, that's all you would need. I have never been asked for anything to vouch for my ESTA's but having read the threads referred to above, I feel better knowing that I have something to fall back on.
If you are able to access a different computer with a printer, all you need is your confirmation number to log into your application and you can then print it at a later stage. In the event that you have forgotten to do so by the time you read this, don't panic, as there is now an option to search for your confirmation by supplying information like passport numbers etc.