Pros

- Strong dueling + teamfighting
- Turret melter
- Very slippery
- Strong engage + burst
- Insane amounts of AOE
- Scales surprisingly well

Cons

- Weak early game and pre-6
- Dragon form reliant
- Ultimate can take a while to charge
- Weak without ultimate
- Immobile without ult
- Big target = easy to hit
- Not a 100 years champ ;-;

You basically want to spend your whole early laning phase farming. Depending on matchup you might want to farm under turret or permafreeze until 6. Getting Shojin + Hydra is quite literally a necessity before easily winning fights. Of course, if you can punish or have an opportunity to kill, go ahead. You also want to force your opponent out of lane so you can get plates. Shyvana is very good at breaking turrets due to her Q being an AA reset and making your next 2 AA fast.

By the end of the laning phase, you should be able to 1v1 your laner and win most of the time, especially if you have BORK. Focus on hitting towers and clearing waves on the side lanes past the mid point of the map. That way you will constantly be applying pressure to the enemy team and they will have to send people to deal with that. If they don't simply punish them by taking their whole turret.

You can teamfight when you feel like you are strong enough. Your aoe alone will carry fights for the most parts. If you can assist on taking down dragons do so as well since it gives you free resistances. You can even ask your jungle to play for bot side and dragons.

The rest of the time should be dedicated to farming and pushing the sides.

Remember to always use your E before starting to AA the enemy cause the mark that it puts on the enemies hit will allow you to deal significantly more damage. Additionally, this damage counts as magical so if they have armor, you will still do a whole lot of damage.

You don't really want to engage without your ult except if you are vs melee and confident/ahead. You can regen fury very fast by AA or Q the wave. Alternatively, you can eat fruits, hit a random jg monster, etc.

Once you have ult, basic burst combo is as follows:
R -> E, W -> Q -> AA, AA -> Tiamat item -> AA

That combo alone should delete health bars with ease. Don't forget to constantly re-apply your E on the enemies as it deals a lot of damage and make your AA deal bonus %max hp magic damage.

In teamfights, you want to wait for a hard cc ability then you can go in. If you are fed you can initiate instead, but be careful. You can then do the combo. With your extremely high aoe damage in dragon form, you should focus on grouped up targets or the adc if you can dragon behind them and oneshot.

Good luck to all you Shyvana players out there. Let's also hope that the rework ends up being good :)