For Neons: Set the temp at about 78-80, feed the parents live food (infusoria and adult brine shrimp) for a few days. Cover up the aquarium to subdue the lighting and cover the bottom with a plastic mesh. Pull the parents once eggs are dropped and you should be good to go.
Cardinals: In theory, the same way. In reality, they're a lot more finicky about when they decide to breed. I've seen more success with small leafed plants to lay the eggs on, but you also have a higher casualty rate as the parents could polish off some eggs before you find them.