This is a list of what abilities that a Kitsune is usually known to have.

Foxfire:

Otherwise known as kitsune-bi, this is the Kitsune's inate ability to generate fire and/or lightning. This is supposedly generated by rubbing their tails together. Kitsune show an adept ability to shape this, sometimes creating little balls of fire used much like a lantern or a way to scare humans.

Elemental Magics:

Dependant on which element represents the kitsune, it can have various assortments of magic. Earth could control land features and make earthquakes and such, while Wind can create gale force winds and tornados. Those examples are not full examples as there is many more those elements can do. One exception is the Celestial (Heaven) Kitsune supposedly can not only do their magic but can use some from each of the 13 elements, but weaker then the actualelement's equivilant.

Transformation:

Now I am a little unsure of how extended this feature is I have a little information. Kitsune are normally depicted as guising themselves as humans wether to fit in or what not. They also can become full fox or a human with some fox features. I believe this isn't all they are limited to but I don't have any other evidence yet.

Illusion:

A combination of both the Kitsune's magic and mind power. The Kitsune can create a myriad of illusions, not limited by size or appearances. Usually illusions of Kitsune are very convincing because to the Kitsune themselves, it represents a realm of reality for them. Holy men and priest, who seem to have a number of ways to deal with Kitsune, can dispell an illusion by touching it. This shatters the illusion and causes the Kitsune some strain due to its concept of reality being tampered with.