There is several ways to obtain links from the big sites, but as you might understand, the less cost involved the more competition you are facing.
Running good PR effort, might get you the attention (and links) from these big sites. Try not to promote your product as much as providing something that has significant news value related to the site you would like to get featured on. It might be a story of how you are helping in the solving of a problem users are facing, it might be funding news - ask yourself what the users of the big site would LIKE to read, and not what YOU would like them to read. Typical mistake in PR campaigns, is focusing on features instead of benefits.
Adding social bookmarking to your website, might help as well, but again ask your self what the USERS would like to share, and not what YOU want the users to share. In the past, providing valuable easy-to-digest content like infographics was the way to go.