I have played Shyvana since she came out now and i have found her to be an amazing champion to play a tank/offtank. This is a build i have developed over the months i have been playing her and my game stats have benefitted massively from it. Most of the time i play Shyvana i play solo top, which is ridiculously strong. I dominate most of my lanes pretty early with my early Warmog's.

Runes

Take attack speed marks, health per level seals, cooldown reduction glyphs and health regeneration quintescences. This will give you good early game sustain with the health regeneration, and your attack speed and cooldown reduction gives you a lot of oppurtunities to use your Q (Twin Bite) in lane, and harass the opponent. The health per level will give you better sustain farther into the game, which, from my own experience, is very beneficial when being taken down to very low health mid game.

Masteries

For masteries, i take 4/26/0, which is a very tanky mastery setup. Which is a great choice for this champion, because she is a great melee fighter who scales well with tankness. I basically take every damage reducing mastery in defense, mastering my exhaust and getting a little bit more attack damage in offense. I leave my Utility tree untouched in this guide.

Items

Start off with a regrowth pendant and a health potion. Try to stay in lane at least until you can afford a giant's belt. If you have to go back and can't afford it, i would just buy 3-4 health potions and wait. Trust me, it's worth it. Then buy Warmog's armor as soon as possible. If you feel you have to buy boots somewhere in between items, you can also do that, but i find my W (Burnout) enough until i finish my Warmog's. Then go straight and buy yourself a Chain Vest, and rush Atma's Impaler. By then, if you are still laning, and against an AD champion, you will most probably dominate your lane at that point. After the Atma's get Mercury's Treads to get a little magic resist and tenacity. And because Shyvana unfortunately has no crowd control, i go straight for Frozen Mallet. Start with the Phage, to get that 25% chance slow which can sometimes be crucial. At that point you should have about 3.500-4.000 health, which is quite good for a melee fighter. After that i get some magic resist and a lot of health regen through Force of Nature. Or if you are against a large quantity of AD champions, you can just go for Thornmail instead. With this you are getting quite hard to kill for the enemy team. So they run away. But they won't get far when you finish your build with Phantom Dancer, giving you the movement speed needed to catch up with your opponents and slowing them with your Frozen Mallet. That also gives you quite an attack speed buff, which can be very beneficial to you in fights, because your basic attacks lower the cooldown on your Q (Twin Bite) so you will be using that a lot when you have that. It also helps you build up fury to cast Dragon's Descent with less delay.

Skill Sequence

I take W (Burnout) at level 1 for that crucial speed buff wherein you don't have any boots, and constant damage to those near me. It's also great for early game minion farming. I max it as soon as i can. I take E (Flame Breath) at level 2 for that little lane poke on the enemy. It can also finish off enemies that are near to death. I max it as soon as i finish maxing Burnout. I take my Q (Twin Bite) at level 3 to be able to put out a little more damage every few seconds. I use it alot to last hit minions and on turrets. As with all ultimates, i take Dragon's Descent at levels 6, 11 and 13.

Summoner Spells

I take Heal and Exhaust for summoner spells, because as i said, i play solo top most of the time. I know some people look at heal and call other players noobs, but i don't care. It saves me from death so many times. Most often i don't use it until i am very low, so maybe if they tower dive me, i heal there, and i take them down under the safety of my turret. I take exhaust to chase down or get away from enemies. I also use it a lot in duels. And it's quite good in the formerly mentioned method of luring enemies into tower dives, and exhaust them under my turret, and kill them.

Summary

With this build you should be able to outlane most opponents on solo top. It's tanky, it's fast and deals tons of damage. What more would you want?

Pros / Cons

Pros:

She can get away very easily if getting ganked with Dragon's Descent, Burnout and Exhaust.
She's a great chaser and most often capturer of the prey by the time you have finished your build.
Moves fast.
Great escape methods. Easy to get away from dangerous situations.
She turns into a dragon.