There are several ways to accomplish this, both within the browser and within the site.

Within the browser:

• you could load the story and add it to your favorites / bookmarks (depending on which browser you use), and possibly organise them into a "Stories" subfolder.
• Alternatively, you could open them up as new tabs - some browsers have a built-in session manager which will restore the tabs that were open when you closed the browser.

Within the site:

• at the bottom of each story, you'll see an "Add to favorites" link. That adds it to a list of favorites stored on the site itself. To view the list, click on "My account" in the right hand sidebar.
• You can also Bookmark stories, and view the bookmarks via the "My bookmarks" link.

Although the two appear to have similar functionality, Bookmarks are private (i.e. only you can see them), whereas favorites can be viewed by other users (to view someone else's favorites, click their nickname in the "Submitted by" section at the top of the page - you can also see how long they've been a member and by clicking the "Track" tab, see the stories they've interacted with recently).