Traditional rivetting is a skill our society has almost completely lost in the last 40 years or so, because of the invention of the pop-rivet. Just to make it perfectly clear, DO NOT USE POP-RIVETS: THEY ARE COMPLETELY WRONG. And don’t use "split" rivets on a helmet, either - they’re not strong enough.

The traditional rivet is shaped like a short nail. When you want to join two pieces of sheet metal, you drill a hole through both, and stick the rivet through the hole, with an exposed end (in our case about 2mm long) sticking out through the hole. Then rest the rivet head against a large heavy piece of steel like an anvil or a steel stake, and hit the exposed end (not too hard) on all sides with a ball-pene hammer, going round and round until you’ve turned it into a domed head on that side. This pulls the two pieces of metal together tightly, and squashes the rivet sideways so it fills the hole completely and won’t rattle around.

    (i) domed-head rivet                                   (ii) cut-down nail

You can use either commercially made domed-head rivets, or you can make your own from flat-headed nails. Either way, you usually have to cut them to length so the right amount of the rivet sticks out of the hole. (Too short and you can’t form the head; too long and the rivet bends and won’t squash sideways.)

The procedure with both is pretty much the same, but a domed-head rivet has the head on the outside of the helmet, which means you can rest the helmet against a large flat surface and hit from the inside of the helmet (Note: if you want the head to keep its domed shape and not get flattened, drill a hole in your big piece of steel the same diameter as the rivet head and a tiny bit shallower, and rest the head in the hole when you hit the rivet.)

With a cut down nail, the head is on the inside, so you have to use something like a narrow stake for the head to rest on, so it will fit in the helmet. Unfortunately, this often means the rivet slides off the stake and falls through the hole just as you’re about to hit it from the outside. However, nails are much cheaper than rivets, and usually easier to get hold of.