Life size, or puppet size?
Depends on the style of helmet. I've made a full size pot helm from cardboard, which was possible because it had a flat top and sides that could be made with a simple curve rather than a compound curve. Also a Japanese Kabuto, which I made from lots of strips of card to shape the top. The same method would work in miniature. These cost pretty close to nothing, mostly recycled card, a bit of paint, some glue. A couple of pics of similar helmets from the internet showing what can be made by bending strips of flat metal or card:
For a helmet (or anything) with compound curves, I sculpt in plasticine, then make a fibreglass mould in 2 halves usually, and cast in fibreglass. Less cheap, but for some shapes that is pretty well what you have to do.
In miniature, the amount of fibreglass required would be so small, it wouldn't cost much. In fact I would most likely make the mould from silicone rubber, since it would only need a small amount.
Sorry! I should have specified. Miniature. Would you do armor in the same way?
Hi. Have a look at the thread I posted called EVA foam helmets. I made some miniature helmets using 2mm EVA foam, effectively a scaled down version of the cosplay stuff. It works well, and can be glued together with contact adhesive. Coat with PVA then paint with acrylics.