There are those few dragons in Runeterra who have mastered the intense magical energies that course through their unique anatomies, evolving into an elusive Celestial Dragon. These powerful and enigmatic creatures spend most of their time hidden away from the lands of men. However, there are those who find themselves drawn to civilization and who take on human forms to immerse themselves in the world of humans. Occasionally, one finds itself drawn to the spirit of a human and they have relations. Sometimes, in the slimmest of odds, the union will bear fruit and that offspring will be one of the few half-dragons to have graced Runeterra. Shyvana is one such creature, born to a simple Demacian farm-girl and her Celestial Dragon father. Left to be raised by her mother, her oddities were something that couldn't be hidden from her community, though she was protected by her family. Once her family had perished in disaster, she was left alone for the first time – truly alone. Shyvana quickly became an outsider and it wasn't long before the community's fear began to put her in danger. Facing mortal danger at the business end of an angry mob, she was rescued by the traveling noble, Jarvan Lightshield. The noble was a man who strangely knew exactly what she was and took her under his wing. It wasn't long before she was offered a chance to use her natural skills in the service of Demacia, as Jarvan initiated her as one of the elite guard. Following Jarvan into the League of Legends was only natural.

Shyvana is a fierce warrior, with the blood of one of the most powerful magical predators in all creation flowing through her veins. Unlike some of her fellows, she is a subdued personality – somber, cool, and collected. However, when the moment strikes, her draconian heritage manifests and there are few that can stare her in the eyes and not feel the primal urge to flee.

“By the blood of my father, I will end you!”

So Basicly, this is the build I use, because sometimes you're forced to act tank or jungle.
So I use this build to get a balanced health, defense and at the same time abit of damage. It all matters to the enemy champions aswell. If it happens that you need more damage output you can Swap the Wriggle's Lantern for a Bloodthirster. This build is also depending much on your team. Don't forget, IF you're going jungle instead of lane change Ignite for Smite (ALSO THE MASTERIES)

Pros
: Very Durable
: Frozen Mallet allows chasing easy
: Wriggle's Lantern allows easy farm

Cons
: Not very high damage (unless swapping Wriggle's Lantern for Bloodthirster)
: Expensive build and not recommended for first time players

At the start of team fights you can go nuts and initiate if you want to.
I personally don't use the Dragon form untill I get a chance to drag someone with me to my team or if I'm versus a Malzahar or some other channeling champion (used to interrupt). After ultimate is done I wreak the team's morale with Burnout and Twin Bite, Using the Flame Breath to lower armor on the enemies, just try to attack as much as possible to keep burnout up and focus the weaker champions because of your lack of damage.

If you chose to go jungle I start with the following

Golems
Wraiths
Wolves
Gank top or Bot depending how the situation is.
Teleport Back to pick up Long Sword.
Then go back and repeat the previous untill you're strong enough to roam.