One of Storm Neos' greatest weaknesses is that in using it's effect, you are likely to destroy the "Neo Space" that would keep it on the field. Keep an "Instant Neo Space" or two handy in case you have to destroy your "Neo Space".
Thanks to recent cards, however, it is possible to keep Storm Neos on the field and destroy your opponent's Spells and Traps without having to worry about "Neo Space" too much. "Dewloren, Tiger King of the Ice Barrier" can return "Neo Space" to your hand, as well as any other face-up cards that you do not want destroyed, and allow you to play Neo Space again, preventing Storm Neos from going back to the Extra Deck.
While equipped with "Instant Neo Space", you can wait until your opponent's end phase to activate his ability to send himself back to the Extra Deck, thus clearing the field, leaving them wide open (Still, watch out for the above mentioned counters).
Summon "Elemental HERO Storm Neos" first, activate it's Effect, and then play "Neo Space"/"Instant Neo Space". If you end up destroying "Neo Space", you can still get it back with "Neo Space Pathfinder".
"The Despair Uranus" is useful to pair with this card in order to protect your own Spells/Traps from the latter's destruction effect.