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.
Dragonborn
Shyvana gains 5 / 10 / 15 / 20 armor and magic resist. These bonuses are doubled in Dragon Form.
Twin Bite
Cooldown: 10 / 9 / 8 / 7 / 6
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. Shyvana's autoattacks against non-structures reduce the cooldown of Twin Bite by 0.5 seconds.
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 trigger on-hit effects and grant fury twice.
Second Strike Physical Damage:80 / 85 / 90 / 95 / 100% AD
Burnout
Cooldown: 12
Active: Shyvana surrounds herself in flame for 3 seconds, dealing magic damage to enemies within 162.5 range each second and gaining bonus movement speed. The bonus movement speed decreases by 15% of its original value per second. Shyvana's autoattacks extend the duration of Burnout by 1 second, to a maximum of 4 extra seconds.
Dragon Form: Shyvana now scorches the earth where she walks, leaving a trail of fire for 5 seconds that will continually deal the same magic damage per second to enemies that pass over it.
Active: Shyvana unleashes a fireball that travels in a line, dealing magic damage and marking enemies hit for 5 seconds. Shyvana's autoattacks against marked enemies deal bonus magic damage equal to 2% of their maximum health (max. 100 vs. monsters).
Dragon Form: Flame Breath engulfs all units in a cone in front of Shyvana.
Passive: Shyvana's basic attacks generate 2 fury, even in Dragon Form or against structures. While in human form, Shyvana passively generates fury every 1.5 seconds.
Fury gained per 1.5 seconds: 1 / 2 / 3
Active: Shyvana transforms into a dragon and dashes to a target location. Enemies along her path take magic damage and are pushed toward her target location. While in Dragon Form, Shyvana's fury decays at a rate of 5 per second. Once her fury is depleted, she will return to her normal state.
Dragon's Descent has no cooldown or initial cost but can only be activated when Shyvana has 100 fury.
6300 or 
975
Edit
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 
