I am going to make a wall hanging for the first time and am trying to figure out when/where to add the interfacing. Is it as I sew the pieces together or after it is all pieced?

I've never made a wall hanging with interfacing. I use batting as the middle of the quilt sandwich. The batting is used after you have assembled the quilt top.

Interfacing is not a requirement for a wall hanging , but it does give a body/ or structure to the wall hanging.
It would make the seams a bit bulky if you used it in the pieces, particulary if you press all to one side.
If it was me , I might be tempted to sew it as I was piceing but press the seams open, this would give each piece the support you are looking for. If you want to add it prior to the backing it wall not support or add much to each piece , acting like an additional layer but primarliy where it is stitched.
If you used a dense thinner batting , I sometimes use the wide poly felt and machine quilt , it has wonderful body , and the use of interfacing would not be neccessary.

Thank you so much for the information. It was just what I was looking for.