Shyvana's abilities have no cost related to them, and the use of her abilities is only limited by cooldowns. Instead she uses Fury as her secondary resource.
Fury is only needed as a requirement for the use of her ultimate Dragon's Descent, which allows her to change form if she has 100 Fury and remain in that state for as long as she has Fury. Shyvana won't generate Fury unless she has at least one point in Dragon's Descent, and once she puts the first point on the skill she will gain 100 Fury immediately. Any gained Fury cannot be lost except by depletion during Dragon Form.