How to properly add another outlet off this box?
Tie into the existing nuts for the pigtails

You'll notice that the hot and ground are pigtailed already -- simply nut the new black and bare wires into the existing junctions.  As to the white wire, it does not appear there's a pigtail for it, so you'll have to make one from a short length of white wire of the appropriate size (if in doubt, get a piece of 12AWG stranded THHN from the hardware store) and nut the existing white neutral with the new white wire and the white pigtail, then connect the new pigtail to the silver neutral screw on the receptacle.

Don't forget to stick a flag o' black electrical tape on the white wire 
that's connected to the various black wires while you're in there -- that will make it plain what that white wire is doing if things need to  be undone again!