Shyvana's abilities don't have any cost related to them, so the use of her abilities is only limited by cooldowns. Instead she uses fury as her secondary bar.
Fury is only needed as a requirement for the use of her ultimate, which allows her to change form if she has 100 fury and remain in that state for as long as she has enough 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 fill the bar immediately. Any gained fury will not be lost until her ultimate is used.
Fury of the Dragonborn
Shyvana's melee attacks enhance her abilities.
See: Fury of the Dragonborn entry in each ability's description.
Active: Shyvana's next autoattack will strike twice in one swift movement. The second attack will deal physical damage equal to a percentage of her total attack damage. Both attacks will trigger on-hit effects and Fury of the Dragonborn effects.
Dragon form: Twin Bite will damage all units in front of Shyvana when she uses her next autottack instead of just her target. Each unit hit will be dealt on-hit effects and grant fury twice.
Fury of the Dragonborn: Each auto attack reduces the cooldown by 0.5 seconds. This doesn't work on structures.
Second Strike Physical Damage： 80 / 85 / 90 / 95 / 100 % of attack damage
Active: During the next 3 seconds, Shyvana will deal magic damage each second to nearby enemies and her movement speed will be greatly increased. Shyvana's movement speed bonus itself will be reduced multiplicatively by 15% for every second that passes.
Dragon form: Shyvana now scorches the earth where she walks, leaving a trail of fire for 5 seconds that will continually deal magic damage to enemies that pass over it.
Fury of the Dragonborn: Each auto attack extends the duration of Burnout by 1 second to a maximum of 4 extra seconds. This works on structures.