Adding favorites in Stringer is easy. Long press on any currently playing cover art in your String and you'll see two options: delete and favorite. If you slide your finger toward the star, you'll be asked what exactly you want to mark (song, album, or artist) and the app will add that selection to a list that the keeps for you. The album art will be badged in your String so that you can see that status at a glance.
Favorites are essentially a subset of your music, they don't function like up/down voting on other services. If you favorite something, it's just marked as such within the app. Later, if you want to create a String using only those selections, you can do so by opening the menu in the lower right hand side of the screen and selecting "Favorites" under the "New String From.." option.
When you mark something as a favorite, You can unfavorite something in the same way (long press, slide up to the star again). This just removes the song/album/artist from that subset.
The favorites feature is available as an unlock via in-app purchase.