Ninetales takes 2X damage from Rock, Ground, and Water attacks.
It takes half damage from Bug, Grass, Steel, and Ice attacks.
It cannot take damage from Fire attacks > upon getting hit, its Fire-type power is increased by 50%.
All other types hit normally.
Ninetales learns a variety of attacks of the Grass, Fire, Psychic, Normal, Dark, Steel, Ground, and Ghost types, so it is super effective against types those attacks are good against, but only four moves, obviously. Ninetales can also learn Hidden Power, which can have any type.
Also, you spelled Kyuubi wrong.