Most neon and cardinal tetras are bred in Asia.
fifefish has is right with sexing neons, male have a straight blue line. Male cardinals & neons are slimmer than females, which get fatter due to the eggs they are carrying.
Keep them all in a group while conditioning them and after a few weeks of good food, then separate males and females for a week. After a week put a pr of fish into a tank about 14-18inches long. Have a layer of marbles and some Java Moss on the bottom. Have a small air operated sponge filter in the tank.
If you breed them in a group they often eat the eggs. This is because not all the fish will breed at the same time and those that aren't breeding will eat the eggs being laid by the others.
The tank water needs to be very soft (GH below 50ppm, preferably below 20ppm) and slightly acidic (PH about 6.5). If there is too much hardness in the water the eggs don't hatch.
The eggs are photosensitive and will die if exposed to light. Therefore the breeding tank should not have a light on it and once the fish have bred and been removed, you should put a towel or blanket over the tank until the eggs have hatched. Then you can remove the towel and leave the tank with normal room light. Don't put a light unit over the fry until they are at least a few weeks old.
The fry are small and do best when fed infusoria and fine baby foods. After a week or so they can get newly hatched brineshrimp.
Put the fish in the breeding tank in the evening and remove them the following day. They usually breed in the morning and can be taken out about lunchtime, sometimes sooner. Observe them and when they no longer show any signs of breeding, then remove them.