Burnout provides the largest bonus movement speed at the start of the ability. Activating it gives a quick burst of speed that can be used to juke skillshots and enemies.
Dragon's Descent is an excellent peeling ability, if you see a key member of your team (an ADC or APC) starting to get focused, use the dash the knock the enemies off while giving your ally enough distance to continue attacking.
With good positioning, you can use the ability to push enemies away from your allies while diving onto their backline to disrupt them.
Take note that stuns, silences, snares, knock-ups and knockback effects can hit and stop Shyvana mid-flight. Beware of your enemies' capabilities to do these.
Dragon's Descent is one of the longest dashes in-game, as such it allows going over large walls and otherwise impassable terrain.
Since patch 3.9, Flame Breath passes through units. If you find yourself as a laner (most likely top) putting points in this ability gives you a good harassment tool and can be used to farm easily. It may be worth maxing if you are against a ranged opponent as Shyvana has no other ranged abilities.
To perform a quick harass, hit your opponent with Flame Breath and run into them with Burnout, following with a Twin Bite to proc the mark twice, putting out good damage and extending Burnout. You can then use the prolonged speed boost granted by Burnout to escape just as you entered.
When using Dragon's Descent, try to position yourself to be able to hit as many targets as you can with your AoE abilities.
Shyvana's kit allow her to do large amount of damage over time at close-range, but it doesn't provide her with burst capabilities. Failure to combine or land Shyvana's abilities together to effectively damage a target will create an opening for a period of time that your opponents can take advantage of, so be aware of your enemies' potential methods to disengage from you.
Sunfire Cape is an excellent item for Shyvana in the mid-game, combining a generally effective chunk of durability stats to survive combat with a good amount of free magic damage to stack with Burnout.
While it may seem odd, Abyssal Scepter will make her highly resilient to magical burst, and vastly boost the damage Dragon's Descent and Flame Breath because they scale with AP, but also of Burnout as it deals magical damage and the scepter aura reduces MR
Tiamat and its upgrade, Ravenous Hydra, can be great cost effective items for Shyvana, offering attack damage, sustain with health regen and life steal along with the active and passive effect, which synergizes with Shyvana'sTwin Bite, procing twice on a single target.
Twin Bite during Dragon's Descent will only proc the passive twice on the primary target due to an intern timer preventing it from affecting multiple targets in one attack.
Shyvana is one of the fastest junglers, having great clear speed and mobility, allowing her to counter jungling exceptionally well. However, her lack of CC diminishes her early game presence and is more focused on denying the enemy jungler.
Overall, it is better to build magic resistance over health and armor to counteract her kit's magic damage, though attack speed slowing items such as Frozen Heart and Randuin's Omen may help to lower her damage output considerably.
If you notice Shyvana using her Dragon's Descent, move away from the spell path to avoid it damaging you - at full range, it will take her 1.3 seconds to reach you so you usually can hope to dodge it from a long distance.
If you have stun, silence, snare, knock-back or knock-up abilities, use them quickly on Shyvana when she casts Dragon's Descent to stop her mid-flight.
Take note if Shyvana'sfury bar is full while you are attempting to kill her. The long range of Dragon's Descent can easily allow her to go over walls even while a fair distance away from them, so avoid wasting abilities with significant cooldowns and costs on her.
Dragon's Descent is not limited by cooldown - quickly gaining fury allows her ultimate to be ready long before yours if you misuse it.
Dragon's Descent requires fury, which is quickly gained by Shyvana auto-attacking. This time period is a good opportunity to harass her from range and delay her ultimate.
Shyvana shines in an extended close-combat fight over time. Use champions with many options to disengage and do your best to avoid such a fight against her.
Shyvana has no natural ways to keep you in place for her to auto-attack you. After using Dragon's Descent, she has little ability to catch up if crowd-controlled out of melee-range. Using crowd-control effects to hinder her movement during Burnout can also stop her from getting the ability to its maximum duration or damage.
Burnout provides a very large amount of bonus movement speed at the beginning of the ability, which decreases a bit in effectiveness over time. Try to avoid using skillshots against Shyvana until after she casts Burnout, as the movement speed boost, especially at the ability's initial use, can allow her to easily dodge them.
Shyvana tends to jungle and normally, Shyvana's jungle route starts at red. Thus, considering stealing her blue is a likely safe method to take experience away her early jungle and to prevent any enemies from having it.
In her dragon form, Shyvana is more powerful than during her human form.
Beware overextending into tense situations to chase her in her dragon form. Burnout increases her movement speed to make catching her difficult and leaves a fiery trail that can deal significant damage if you do not avoid it.
Following the burning trail allows you to find her easily, but you also take DoT - if you and Shyvana are both fairly weakened, underestimating the DoT can firmly put the tide in her favor.
Shyvana lacks any gap hard gap closers across from her ultimate, Dragon's Descent and she is highly dependent on her movement speed with Burnout to get into range into the enemy. As such, ranged top laners with good kiting mechanics such as Teemo, Kennen, Jayce, Nidalee, Ryze, Lulu, and Kayle can easily zone Shyvana out and can harass and farm safely in a distance.