No, I am not a pro, I only just hit level 30. However, I always see Shyvanas do really terribly and I would like to try to remedy that. This is not a perfect build, however, it works for me. I really like this champion and I feel like she is really strong. If you have any suggestions, message me. I am always open to new ideas.

Pros:
Very fast creep clearing
Does not need blue buff
Gets very tanky with just a few items
Very early dragon threat
Scales well in to late game
Cons:
Weak ganks
Needs Red buff

For runes I take 9 Armor Penetration Marks, 9 Flat Armor Seals, 9 Scaling Magic Resist Glyphs, and 3 Attack Speed Quintessences to help you early on against jungle creeps.

I take standard 9-12-1 mastery's, making sure to put a point in buff duration mastery. I also take a point in the exhaust mastery to help Shyvana's ganks.

I start Cloth Armor and 5 Health Potions. After doing my first clear, I go back to base and buy Boots, spending my leftover money on more health potions. Then, start building your Wriggle's Lantern and Wit's End. After those two items are finished, build Mercury's Treads to keep from being kited. Then i build a Frozen Mallet, because of the bonus health and the synergy of the slow with the speed boost from Shyvana's W. After that I build a Atma's Impaler for more Critical hit chance as well as Armor. Guardian's Angel is icing on the cake, giving you extra armor and magic resist as well as the ability to come back to life if you get focused.

I max W first to help clear camps quickly. After that I max Q for more damage 1v1. I put 1 point in E at level 4, just for the armor and MR shred. And of course, take points in Dragon form when you can.

I take Smite, of course, as well as Exhaust, as Shyvana has no CC except for her ultimate, so Exhaust improves her ganking potential before Level 6 greatly. Flash is always useful in helping you escape if you have a hard time getting caught when counter jungling.

I start blue buff at level 1. With a proper pull, you should have no problem killing it. Then I move on to clear wolves, wraiths, and double Golems. I then go back to base and buy Boots and more Health Potions. Then I grab Red buff and re-clear wolves and wraiths. By then, you should be level 5, at which point you should start looking for pushed lanes and easy ganks. Just keep clearing your jungle and ganking lanes. Just keep clearing jungle camps and ganking lanes. Make sure to feed blue buff to your mid, as you do not need it after level 1.

Shyvana can be played many different ways in teamfights. She can initiate, clean up, or provide mid-fight damage. If you get fed and get your Frozen Mallet by the 25-30 minute mark, don't be afraid to dive in to the enemy team. However, if you do not get your Frozen Mallet by that point, wait for your tank to initiate, then use your dragon form to jump on to their carry. Dragon's Descent is your main teamfight skill, it can initiate, or let you escape if the teamfight goes badly.

Dragon's Descent transforms you into a Dragon, and gives you a whole list of different skills. These changed skills, while still the same, have added affects that give them more teamfight potential. Twin Bite and Flame Breath both do AOE damage, and Burnout leaves a trail behind you that does damages over time. These added effects make you much stronger when fighting multiple champions.

Shyvana is a very strong champion. She deals lots of AOE and single target damage that makes her very good in a large teamfight. She is one of the fastest junglers in the game, and while she has weak ganks, even 1 or 2 early kills help her scale in to late game extremely well. She is definitely a champion that I would recommend picking up.