Shyvana seems simple, but thats deceiving. Her kit is very straightforward, but it doesn't allow consistent play. Mastering Azir is learning how to play him and all of the intricacies of his kit. Learning how to use Shyvana's kit is easy, applying her strengths to a game is hard.
Don't gank, Shyvana is not good at it. If the enemy is making love to your laner's tower, then show up and put a boot up their ass. Counterganking is also good. The enemy is less likely to back out if there are even numbers.
Don't go full tank. Shyvana has no impact outside of her damage. If she does no damage then the enemy team can ignore her until the rest of her team is dead. You need at least 2 damage focused items. Bloodrazer jungle item + Choose One (Trinity Force, Blade of the Ruined King, Titanic Hydra)
Do focus on objectives. You see the enemy jungler top lane? Go take dragon (Shyvana can solo it post lvl-6 if she has Bloodrazer or at least a Recurve Bow), go take all of the enemy's bot jungle, so force a gank bot to take their tower.
Do split push. Shyvana is exceptionally good at splitpushing because of her love of attack speed. If you have a Tri Force, you have bonus points in the split push category. Another reason she is good at it is because she is really good at dueling. If only one person shows up to stop you, unless they are a better duelist like Yi, Jax, or Trundle, you will probably beat them. If they send more than one, then your team has more pressure else where on the map. (When i play it sometimes takes three people to bring me down)
EDIT: In case you can't tell from the other comments. Don't listen to MaropaL2. He is just trolling.