Dad had a chinese copy... Won't light very well, goes out... Not as good as the genuine item... Wonder if they make them cheaper by skimping on the platinum catalyst?
Since the catalyst is the only thing that makes it work, if they skimp on that they might as well just sell you a leaky bottle to hold the fuel!
With the (genuine) Zippo I've noticed a definite reluctance to start when the thing is really cold, but I just heat it gently all over with a blue flame lighter before lighting it. Don't go overboard if you try that, it just needs to be fairly warm to the touch.
Occasionally also I've found that if it's cold it may go out the first time it's lit, but it seems to be less likely to go out if it's carried upside down. Fuel vapour is heavier than air I suppose.
To light it I usually first put a couple of drops (no more than that) of fuel on the catalyst. It burns with a sooty flame for a few seconds, then that flame goes out leaving the catalyst glowing red.
You can see that it's burning if you look at the catalyst in the dark, it will clearly be glowing red if it's burning properly.
A couple of people that I've seen who were new these things haven't read the instructions and have tried to put the fuel into the catalyst instead of removing that part to get at the wadding beneath it. They've damaged the catalyst beyond repair that way.
Some of the clones have a separate filler hole (I have one like that from Whitby Knives) which seems to be a good idea unless you lose the little plug, or it falls to pieces which is what I expect to happen to mine.