Then you will see that by the number on the left it will show the "# of diggs" and a link for you to "digg" a story. When you click it then you have "dugg the story" and you get your free text link.
Digg is a very very high traffic "tech" site just like what slashdot is and basically if a site gets enough "diggs" then it will be promoted to the front page news.