Prior to riveting, I first make sure I've filed the surfaces and have good tight contact on them. I also make sure that all bending of the parts is finished.
I use a number 6 soft iron finishing nail (not the "bright" ones) and a 7/64 drill bit. I drill a hole straight through the face of the plate, about a quarter inch from the top edge, and centered. I then drill through the top of plate, eye-balling the angle I need for the hole. That hole is also about a quarter inch from the rear of the piece, and centered.
Then I countersink the holes, cut the nail to length, and peen it in.
for the actual peening... I leave the nail long and insert it from the top of the plate. I put the pieces on the bench vise with the long part of the nail clamped in the vise, and peen the head of the nail in the countersink on the top of the plate. Once I have that one done, I cut the nail, and set the plate up in the vise with a piece of 3/8 inch thick iron bar, as shown in the photo. The holds everything steady while I peen the cut end into the countersink on the face of the plate, and it provides a very rigid surface on the other side of the rivet (nail) to peen against.
Once riveted, everything fits nice and snug. The two parts can be moved, to ensure proper alignment, but they're tight enough they don't move on their own.
I hope that answered your question.