First off, this isn't my build, I got the item, runes, and masteries off GreenEyedMonster from a LoL discussion board. I have also not tested this guide in ranked games, so just a heads up. I decided to compose it on here because I have used mobafire a lot and I wanted to give back. Also, all other guides have bad reviews, so, hopefully I can spit out a good one. I'll try my best to explain items and skill choice from my experience with Shyvana. Let's get started shall we?

Exhaust: I use this for chasing, or even engaging if I want to drop another champion before he can run to a tower/team. I use it less after Frozen Mallet, but that's not to say it isn't used.

Flash: From my experience, this spell has been more helpful to chase or engage than escape, I usually burnout of the area after the kill.

I haven't reviewed other summoner spells with Shyvana (with the exception of Garrison in Dominion) so I am not entirely positive on how they will work, any feedback to add to the guide is valued and encouraged.

I always start with a Doran's Shield early game for survivability. I stay in lane until I can afford both Vampiric Scepter and Boots. I leave the lane again for Wriggle's Lantern for the ward and damage, and Berserker's Greaves for attack speed.

Note: If you are facing a team with a lot of CC, it's usually better to build Mercury's Treads.

After your boots, save up for a Phage and eventually Frozen Mallet for damage and the slow. On top of chasing, the slow is important for Shyvana's passive buff to Flame Breath.

After FM get a Zeal for attack speed and the movement boost.

After Zeal, buy Atma's Impaler for damage, then upgrade zeal to a Phantom Dancer to further increase your AS and MS. You should be getting a good number of kills now, so buy a Bloodthirster to finish your build off.

I pick up all the spells as soon as I can, Burnout is first to get in and out of range when harassing or ganking early game. Burnout is maxed first for the mobility and passive damage for chasing.

I then grab Flame Breath, which is maxed second. This skillshot is good for the armor reduction, and it is very good at harassing and even picking up kills if used right. It's maxed second purely for it's damage. It's damage is also boosted against debuffed enemies by 15%, which works well with Frozen Mallet.

Last but certainly not least of regular skills, Twin Bite. My personal favorite because of the damage it can deal late game. Now you're probably asking, why max it last if it's my favorite? It's because Twin Bite doesn't have a considerable damage boost until you get good items, since the attacks scale off your AD, low AD=low Twin Bite damage. Early game it's mostly used to keep Burnout up.

Shyvana's ultimate, Dragon's Descent, has a passive bonus to armor and magic resist, which is why I don't build her as a tank. In my opinion, as long as you're not the team tank, your health, armor, and Mr will be high enough from her ult and the item set I've layed out.

Onto the active part of her ultimate. While active, it will double the bonuses to Armor and MR given by her passive. Deals aoe damage and carries (very pooly imo) any champs to landing location. Oh yeah and you become a F*CKING DRAGON. Shyvana's Dragon form will grant various effects to all her other skills:
Twin Bite will deal damage in front of Shyvana, instead to one target.
Flame Breath will deal damage to all enemies in a cone aoe, instead one target to the first enemy it hits.
Burnout will leave a trail of fire, damage all enemies in it. Think of Singed's poison, but WITH FIRE.

This build has worked wonders for me so far, and hopefully it will for you too. It was my first guide so hopefully I did good enough. Any questions/feedback/tips/critisism is highly valued (so long as it's respectful.) Don't forget to vote up if you like! GL and HF! :)