How to repair damaged drywall seam
There's really only one right way to do this. It takes a bit of time, but it's not difficult or complicated. 

You'll want to replace the tape to ensure that the seam doesn't propagate through the paint. Pick up some premixed topping compound (available in gallon or smaller buckets), and a short roll of joint tape (cheap enough to not bother experimenting with other types of paper). 

Cut a length of tape just shorter than the repair, then cut 1/4" or so off one edge so it fits comfortably in the depression. Fill the depression with mud using a taping or putty knife, then lay the tape into it. Drag the knife over it to embed it in the mud. 

At this point you can opt to walk away and let it dry, or try and skim over it now to save time. By letting it dry first you eliminate the risk of pulling the tape around or wrinkling it. 

Skim once or twice more, dragging the knife at a low angle and pressing firmly. There should be very little sanding to do if you do this properly.