This is a basic guide on how to play Shyvanna. Nothing fancy, I'm just going to show you the basics. For background information I'm a Plat summoner that started playing League at the end of Season 2. I play for fun with friends, but I tryhard when I play ranked games. My summoner name is UnseenPanda.

PROS:
-Tanky
-Good Initiate
-Require Little Skill
-Hard to be kitted
-Can Steal objectives by going into dragon form and smiting
-Good Dueling and Counterjungling

Cons:
-Easy to count ult (Thresh)
-Needs Items
-Doesn't work in every team comp
-Has no CC, can't lockdown carries

Shyvanna is a tanky jungler that does quite a bit of damage with her base abilities, so with items you want to focus on getting tanky and let your base stats do their thing. Spirit of the Ancient Golem is a must on Shyvanna and Ninja Tabi.

For Runes you want a combination of damage and tankiness.

You should run:
3x AD Quints
9x Hybrid Penetration
9x Armor Yellows
9x Flat MR Blues

But if you do not have hybrid penetration runes (as they are expensive) you can run flat AD reds instead or flat armor reds.

For masteries you want to focus on tankiness and deal lots of damage. Shyvanna does well in the offense and defense tree, but is useless in the utility tree, so do not put any points in the utility tree. I recommend to take 9 points in offense focusing on cooldown reduction and scaling and flat AD, and for the defense tree take 21 points focusing on scaling defense avoiding things that give you flat defense but taking things that give you % defense increases. Avoid block and unyielding, because you are not laning. Avoid taking oppression, because crippled enemy champions should not be doing that much damage. Juggernaut and Legendary Guardian are an absolute must, because Shyvanna goes balls deep when ganking and in teamfights.