Your tank needs to have soft water. Fortunately, where I live is very peaty so our water is naturally soft. If you have hard water, put peat in a mesh bag and put it in your filter and let the tank run a few days. Water should be more acidic than alkaline.
Condition the males and females separately for two weeks, feeding them bloodworm and daphnia (preferably live). After this, put them in your tank but remove the filter. Make sure that the tank is somewhere it can be easily darkened (IE putting a towel on it or something) as Neons tend to breed in darker conditions in the evening. Check every morning to see if they have bred.
Breeding tank - sparse, marbles as gravel for eggs to fall through and not be eaten. breeding mops too!
Do not feed them in the breeding tank - this is unnecessary and will spoil the water. Remove the parents as soon as you see the eggs. The fry will attach themselves to the glass for the first 3 days and then afterwards they will be free swimming. You can feed them baby brine shrimp (best for growth and development) or LiquiFry or pulped egg yolk etc.
Water conditions are important so keep an eye on them. You do not need a large tank to breed Neon's, they'll practically breed in a tub if you have the right conditions and conditioning.
Not the same family but I know someone who successfully bred Minnows in large jam jars!