I have several vintage Jon-e style hand warmers and last winter I picked up a new Zippo Hand warmer to compare it to the older ones.
I have been using the Zippo this past year and can report that it works well. I picked up the black model but if I we to do it again I would get this chrome one. Other then that I am happy with my purchase.
To light you fill the hand warmer with lighter fluid and then put a couple of drops on the heater element. Light the element with a match and let that burn off. Once the visible flame is gone put the top on and you should running well.
The burner works like a catalyst. The initial burn on the heating element causes the lighter fluid to vaporize and then burn in the heating element. Once started they will run until they are out of light fluid, you remove the heating element or they run out of oxygen.
The heating element and shield are only held on by friction. So you may have to tweak them to get a tight fit. On the Zippo I did not have to do this but I did use a replacement element on an older Jon-e and that did require some tweaking.
I have read that you can use coleman fuel instead of lighter fluid but have never experimented with it. If you have please let me know how it works for you.
I got mine from amazon (Zippo Silver Hand Warmer). In the video I said they are around $20 but there are really under $10. At that price they are a killer deal. If you have amazon prime these end up being cheaper Zippo A-Frame Chrome Hand Warmer, Silver
The replacement burners are also available from amazon (Zippo Outdoor Line Handwarmer Replacement Burner (Silver, 2.38 x 5.81 x 5.31)). But at the current price you might as well get a new one.
Vintage ones are common on ebay : http://www.ebay.com/sch/i.html?_sacat=0&_nkw=jon-e+hand+warmer&_frs=1
As promised in the video here is the old manual