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Basically there are 2 ways:
-you use sort of a miniature soldering torch which produces a tiny flame (few mm's), pretty common and cheap. Go around the bottle several times with the flame at a line you've been drawing around where you want to cut it until it becomes red, then quickly put bottleneck into cold water - hopefully it falls off at the desired cut. If you're lucky the botleneck hasn't cracked (what would make it useless), actually 1 of 2 or 3 turns out to be ok.
-some people tell one can do the trick with a cord that is drenched in gasoline; string it around the bottle, light it and then as above (water). I doubt this works, though
Now comes the hard part! You want to have a plain cut edge at least, if not polished. To obtain this, you have to grind it. A grinding machine with a slow turning wheel which is cooled with water works best. When trying this by hand, it lasts for days; with a normal (fast rotating) grinder the glass gets too hot and cracks inevitably. At the very least ths is some hours of unlovely work which isn't rewarding in many cases either; the bottleneck-in-progress can easily turn useless at any time of the process.

I write this because I did it several times even with Magnum (1,5l) sparkling wine bottles, which have very thick glass (that doesn't make ist easier) and have long necks without a curve. These give the best an heaviest bottlenecks (70-80g). I even did one both sides to get rid of the bulky rim at the tip of the bottle - honestly, I don't remember how I managed this (must be 10 years ago) .