Assuming the tank has proper filtration and has a functioning nitrogen cycle and you are doing weekly water changes and maintenance and all that good stuff (is it, or are you planning on doing so?), I'd say 10 normal neon tetras.
You could put a couple more than 10 I'm sure, but it's better to stay on the low side of stocking, and you'd also have the option of adding one or two other fish, rather than cramming it full of neons then deciding you also want a betta or something in there and not having enough room to add it.
With my experience with green neons (cousins of normal neon tetras), they seem to come out more if there is another type of bigger, bolder fish in there. They see it is safe to come out if there is someone else swimming around with them. Something like a betta or a small gourami, one with a very very calm attitude, could be a good choice.
Neon tetras are rumored to be sensitive to water quality and can die off or get sick if added too quickly to a newer tank. You may want to watch out for that and make sure your tank is fully cycled for a few weeks before adding any neons.