You can find the Amazon Prime lending library books online by searching in the Kindle Store for 'prime eligible', then selecting 'Kindle eBooks' from the filters on the left side. Here's a direct link to the full library with more than 160,000 electronic books:
Here is much more limited selection of the Prime Lending Library (about 100 bestsellers):
You must borrow the electronic books from your Kindle device, not from the Amazon website. Instructions for borrowing from your Kindle are here - http://amazon.com/kindlelendinglibrary. Scroll down to the 'How to borrow from your Kindle' section. You can only read the borrowed books from a physical Kindle device, not from Kindle web reader or Kindle app for iPhone, iPod or iPad.
Amazon.com: Customer Discussions: Are "Free Bestsellers" free for only Prime? - http://goo.gl/pu8l7
Amazon.com Help: Kindle Owners' Lending Library - http://goo.gl/daKeE