As the link said, you'll need to condition the neons for a while on high quality foods and make sure you have a very pregant female and mal neon.
You will need a cycled empty tank- preferably 10gals minimum- with no substrate or planting. The reason for this is a because the eggs are so microscopic the male neon can often not find them to fertilize them or the eggs fall between the gravel for example out of his reach.
You will need to cover the tank in newspaper or somthing similar to prevent light from getting into the tank as the fry are light sensitive and thus die in strong light, so total darkness is the best for them. When the fry are born, they are also microscopic and see through- you will pretty much need a maginifying glass to see them; you should feed them liquifry for egg layers and other similar fry foods, the fry will also die off at the slightest trace of ammonia or nitrites.
The parent neons will also eat their own fry so they will need to be removed after they have hatched and that is if the parents don't eat the eggs.
Personally i suggest you go for somthing different to breed, neons are mass produced in asia anyways and are notoriously difficult to breed on a small scale and are basically a pain in the bum to breed and you cannot even properly see the fry for the first half of their lives, but if you want a big challenge, neons are your fish.