If your local town has a shop where children go to make their own Teddy Bear - I think they are called Build-A-Bear - then have a look round their accessories. They used to have a neat little policeman's helmet.
(I've just checked - they still do them but shown on the website as a package with jacket and trousers. Perhaps they are still available individually in store:
http://www.buildabear.co.uk/shop/browsecategory.aspx?Category=Careers
They only appear on the UK Buildabear workshops. The US websites show a different range - no cops!)Otherwise you can make a very simple but adequate one in cloth. Here's one from the 19th Century in blue serge:

Another way is with felt, cut into shapes (elongated triangles with curved sides) and stitched together, then stuffed, in my case with cotton wool. You can then give a coat or two of varnish to harden it up. Mine is very old - the felt has gone fuzzy with age - but it has held its shape for 40 years!

Perhaps the best way is to model the helmet shape in clay or plasticine, then cover with layers of torn up paper. Leave to dry, and then remove the plasticine to heave a lightweight, hard helmet shell. Paint and decorate to taste. I think Chris Panic uses this method:

Professional hat makers do steam and block felt. This is a skilled job and requires special equipment. It is quite unnecessary for our needs.