Welcome to Shyvana-TheDragonAge!!!
I've just recently started to play Shyvana, but i think she's such an awesome Char and she can turn into a Dragon! isn't that cool?!
This is my first Build so I'm open for your improving proposals^^ (especially with the runing, i aint got much knowledge about that^^).

My Build is concentrating on giving Shyvana some Lifesteal as early as possibly so she gets durability and then building up attack speed. With my chosen Items I also ensuring to give her some resis 'cause she's quite squishy at the beginning.
My build is focussing on a strong mid and late game.

My Masteries are 21/3/6.
In the Offense Tree I focus on giving Shyvana as much damage as possible.
The 3 Points in hardiness are giving shyvana some more resis for early game.
The Utility Tree is important for her flash and the increase of movement speed for her is nice in kombination with her aura.

The best summoning skills for her I think are flash and exhaust.
Flash is my main spell for nearly every char^^ so I chose to use it also with shyvana.
Exhaust is very important to Shyvana! 'cause she ain't got any masscontrol-effects and
without exhaust chasing an enemy is a pain in the ***. But im taking Ignite instead of Exhaust because i like Ignite more^^.
Also with exhaust the enemies have to stay longer in your burnout, which is really useful^^.

My first skill is Twin Bite for taking the first blood.
Then I skill Burnout and Flamebreath so i got all her Skills.
Next is one point in Twin Bite and then I try to max Burnout as soon as possible.
I think Burnout is more important to Shyvana then Twin Bite 'cause she's given a great ability to jungle and get more money. Also its important for fleeing from enemies.

At the Beginning i start with boots and 3 healthpotions. You can also start with a Dorans Blade.
Next is Berserkers Greaves.
Now I'm giving her a wriggle's for some lifestael, AD and Armor.
With buidling Wit's End she's getting a lot of attack speed, a nice passive effect and more magic resistance. Now its Trinity-Time!
I think Trinity is the awesomest item for her because her Twin Bite gets something about 300% more damage!!!
Then I take SunfireCape to make her tankier and give her a double aura.
Last is Madred's 'cause its giving her mor attack damage and speed and armor. And the passive effect is nice too^^. Instead of Madred's a Bloodthirster or Black Cleaver is a good alternative.
If the game is not ended already you can sell wriggle's latern for bloodthirster or something like that.