I was never good with intros so I'll just get right into the guide.

Pros:
-RAWR YOU'RE A DRAGON
-STATIKK SHYVANA
-STATIKK SHYVANA
-STATIKK SHYVANA

Cons:
-Zoning AP carries are effective against you, especially since they don't let you push.
-Your ult more or less just cancels others.
-You aren't Braum.

Generally ghost and teleport will help you the most in matches. Ghost will help you escape/get the last hit on enemy champions while Teleport gives you global presence if used right.
Flash is okay, but it's long cooldown and short range reduce it's usability. (You do not want to be using flash to knock back people with your ult when you're by yourself, you'll end up further away from them than you were before).
Ignite is very usual for lane presence, especially if you think you will be getting a kill in your lane. I'd consider it if I'm versing one of the easier people to lane against.
Clarity is your back up spell in case you can't decide.

I cannot express to you the importance of rushing Statikk Shiv on Shyvana. Without it, you aren't really Shyvana, just a hollow copy of something which may be a dragon. If you do however, she will squish your cheeks and go "Moshi moshi!"

The point after you complete Statikk Shiv, you will be able to wave push like a mad drag. Completing Ravenous Hydra will compliment this.

The rest of your build really depends on the enemy team comp, you mainly want to build so that you survive as much as possible during a team-fight. Take into consideration all of your enemies and build defenses appropriately.

End game you should have great than 4200 health and tonnes of anti-damage.

So in the early game you will be weak because you got Brawler's Gloves instead of a useful item, but you don't really need to worry about that because you will definitely reach the goal of being Statikk Shyvana well before your enemy will, especially if you are versing someone who is not playing as Shyvana!

Your best combo is the E, auto, Q, auto. Practice it and you should be able to do it within a quarter of a second. Other combos are:
W, E, Q, run away, if you're scared of a trade back.
E, W, auto, Q, auto, kite if you have plenty of time.
E, R, W, Q, kite if you want to go ham.

During the laning phase you will want to poke the enemy with your combo when they get near your creeps. Decide on whether you should push up against them or try to freeze lane. If you're struggling then use E to get as much cs as possible from a distance.
When you complete Statikk Shiv, your core item(s), intimidate the enemy tower with your seductive scratches until it eventually collapses from exhaustion. When your enemy laner inevitably leaves because Statikk Shyvana op, be sure to call "MIA TOP LANE MOFOS" and start pushing.

You are Statikk Shyvana. This is your domain. You're a food connoisseur, and your favourite treat is the death of small, unintelligent minions and immovable, large objects. You must venture the map and devour all minions on the map, destroy all immobile objects, defeat invisible Teemos and out-kite Malphite.

You are Statikk Shyvana, but you are also the team's tank. Play as appropriate and soak up damage for your team! This is the reason you spent the last twenty minutes eating as many slaves as possible! Only here you should be using your ultimate to push enemies back, as your entire team can follow up, unlike when you're by yourself at top lane, eye off the enemy Nasus.

Enemy nexuses are your favourite treat by far.

Statikk Shyvana op.