To Bookmark a song, click "menu," directly between the "Thumbs" below the album art, and hover over "Bookmark...", then click either "Bookmark this song" or "Bookmark this artist."
Pandora Bookmarks are useful for making a note of a song you want to purchase later, or a song or artist you'd like to read up on at some point. (They also make excellent hint lists for birthdays and holidays!)
You can also see your list of Bookmarks at any time on your Pandora listener
Profile Page. Just click the "Your Profile" button above the left corner of the main Pandora controls to open this Profile page in a new browser window or tab. This Profile page will also open on its own the first time you make a new Bookmark during a particular Pandora listening session.
Note that it's easy to buy individual Bookmarked Songs directly from your Profile Page, using the Amazon and iTunes icon buttons at the end of the line for each Bookmark.
There is also a "Buy All" option in the top right of your list of Bookmarked Songs.