Looking for a related post plugin which slides-in like the one at inc.com does [closed]

The plugin I think you’re looking for is http://wordpress.org/extend/plugins/upprev-nytimes-style-next-post-jquery-animated-fly-in-button/

“Just like the NYTimes button, upPrev
allows WordPress site admins to
provide the same functionality for
their readers. When a reader scrolls
to the bottom of a single post, a
button animates in the page’s bottom
right corner, allowing the reader to
select the next available post in the
single post’s category (the category
is also clickable to access an archive
page). If no next post exists, no
button is displayed.”