For many years, Neon Tetras were considered impossible to breed in captivity. Despite observations that suggested spawning, no fry were ever produced.
In a book from the 60's, Derek McKinnery described his success, which basically involved good conditioning in sexually segregated quarters with outstanding water quality. Followed by introduction of a sexed pair into a darkened breeding tank, spawning occuring in plant thickets at first light the next day - a very typical egglayers strategy.
His method showed that spawnings in water with anything more than 2 degrees of hardness would simply not hatch. The water quality does not just need to be good, it needs to accurately mimic the environment from where the fish are found - in short it needs to be absolutely exceptional - and remain so.
From then on, the techniques have been refined, and Neons are farmed in Singapore, the Far East maybe Florida - not sure, often with the help of hormone treatments.
If you are a beginner to breeding fish, then the Neon is, not quite Mt. Everest, but certainly not something to try on your first outing. One would also have to consider the cheap, plentiful supplies.
It is a fish to breed for the challenge, not really for any other purpose IMHO. That said, I encourage people to take challenges like that - you should however, be aware of what you are getting yourself into.