I know most people just glance through these guides, check out the builds and what not. This one is a bit more in depth and comprehensive. It's not what to build for Shyvana, it's how to play her. She is a completely different character and has a lot of potential. The idea of this specific Shyvana is to be a very powerful solo top at the beginning and an AD carry at the end, if the game goes long enough. I personally can go 1v1 against any solo I have played against with this build. And late game I usually start getting tons of kills. Usually around 20.

Shyv's passive to her Ult allows her to be an AD carry and still be able to survive
With this build you can rack up a ton of kills on still not be weak early game.
She is very fast, and can escape ganks really well.
Did someone say dragon? Yes she is that too

No CC.
She is not a tank and an easy target when in Dragon form
Very susceptible to cc

These runes are to make Shyvana's early game combo do as much damage as possible. Keep this in mind as you use her combo again and again.
(greater mark of strength): This givese you about +9 AD at the beginning. The only skill that technically builds off of this is Twin Bite. But AD is so important early on for her because of the Flame Breath + Twin Bite combo. It has low cooldown and is devastating. Also this build doesn't have any more AD until after the first phantom dancer.
(greater seal of alacrity): pretty darn useful as her passive allows you to use Twin Bite much more frequently. Also once you get to level 6 you will be able to use Dragon's Descent much more frequently.
(greater glyph of strength): same as the mark of strength. Essential early to mid game. The glyphs don't add much AD so they could be replaced with armor penetration.
greater quintessence of desolation(greater quintessence of desolation): This amount of armor penetration will make Shyv destroy opponents early game.

Same goes as with Runes. You could build defense with her, but I suggest no. At level 6 you will get the passive 15/15 from your ult. This should balance out against whatever def runes your opponent has. So with Attack masteries you will be doing maximum damage at an early level and still have a nice armor cushion, to protect from ganks.
Keep in mind you want that early game combo to absolutely destroy opponents.

: Wonderful skill. Don't be too enticed by it though, Sheen will NOT help this skill. Read carefully, it does two consecutive attacks. Not one. So sheen will cause you to do about 3x your original damage with this hit. Don't waste the space with sheen, get Infinity Edge and do some real damage.

: Overly tempting skill. Do not use this on enemy minions, you will push the lane much too fast and end up getting ganked. And do not use it underneath an enemy turret, if you hit an enemy champ you will be targeted. This skill is great for taking out jungle minions and for the passive speed boast.

: Flame breath is great early game. It does a nice bit of magic damage, has low CD, and drops their armor. Couple it with twin bite and you have a devastating combo. Late game it is still good for dropping opponents armor.

: Dragon's descent is great as an initiator, an escape technique, and a last hit. If someone is about to escape and burnout is on CD, just quickly use your ult. Most people say "what a waste" but realize that your cooldown is really, really, really low. With the Phantom Dancer you can have this ready again in no time. Also don't forget it grants you 50 armor, 50 MR in dragon form.

So whilst laning there are some important things to remember. You want to run in strike, run out. So its pretty basic. Throw your Flame Breath (drop their armor) use burnout (get some speed) use your Twin Bite and hit them. There is almost nothing they can do to prevent this from happening. Again and again and again. You do too much damage for them to risk a conflict and you are too fast for them to run away. Do this until they get to about half health and then go ahead and exhaust ignite and destroy. Important things to remember, DONT push your lane. If you do you will get ganked and die. Just last hit your minions and appreciate the Heart of Gold. So I know its tempting but dont use Burnout on the minions.

Here are her good and bad lane opponents:
GOOD
: You are lucky indeed if you are against Nasus. Nasus does not have the damage output to even effect you. Just keep up your combos and punish him if he goes near a minion. Remember he has to farm his siphoning strike so watch where your low hp minions are and strike him when he goes near them. With luck you can completely shut down Nasus. But once you hit level 6, don't commit unless you know you have a huge advantage because Nasus's ult is so formidable.
: Yorick will be able to outrange and out farm you. But you can deal much more damage to him and harass him enough that he has to stay away from the minions. Just positions yourself behind his minions so that you can Flame Breath him if he gets anywhere near. Then last hit the minions and avoid letting him get even experience. If he gets close, use your combo. Late game you will completely dominate him in a 1v1.
: Volibear has a lot of health. But early game he does not do enough damage. Also players often start him with ruby crystal, so he won't have enough hp regen to sustain against a good shyvana. Let him push and then strike. Don't use exhaust till he starts to run, and if his passive starts quickly ignite him to prevent full regeneration.
: Same as Nasus. He does not have the range to combat you and you can just keep hammering him with your combo.
: Rumble isn't too bad, he can out range you but most everything is a skill shot of his. You can trade hit for hit with him and eventually be able to take him down because Shyvana is so much more resilient.
: You will destroy Cho. He is squishy for a top and does not do near enough damage to you. Just dodge his ground spikes and he isn't a problem.

BAD
: Maokai can be a problem. He is very tanky and has some range with his saplings. You can sustain against him but it is hard to kill him or prevent him from farming, his abilities slow you too much and boost his speed too much.
: If you are against a GP that decides to build crit percent or damage, you are in trouble. He can stay out of reach of Shyv's combo and destroy her with the crit shots. If this happens play very far back and use Flame Breath to last hit minions.
: Same as with GP, if he builds crit rates you are in trouble. If he builds the balanced trynd build, you should be able to easily destroy him. Just avoid getting to close in range when he has his fury up. And at level 6 he will be able to kill you using his ult. But Shyvana can almost always get away.
: Sion's CC is going to be really, really annoying. He also has a really high AD because of his Enrage skill. Lastly his shield will prevent you from being able to do any real damage to him. Just keep Flame Breath the minions for farm and wait for your jungler. Or wait until he attacks you under your turret. See ganked section for that.
: Garen's Regen is just too intimidating. He can always just sit in the back and wait for his hp to regen all the way. Also he has the same passive 25/25 armor and mr. You will need your jungler to take down Garen.

Getting ganked? This is why Shyvana is the best solo. If you are not level 6, use your Burnout to get away. pretty easy. Its doubtful they can kill you if you keep your health regenerated, Unless its a huge amount of CC. Anyways, you can easily turn their gank to your advantage. Lure them close to your turret before you use burnout. You want them to tower dive. Whoever the turret targets first hit with your Flame Breath (drops their armor and the turret will now destroy them). Now use Burnout and run quickly around the turret. Your opponent will be dead before you know it.
If you are past level 6 and you get a hard gank, just Dragon's Descent out ( you will get a nice jump and you will get the extra armor/mr) and then use Burnout. Even if they follow you they will take a nice bit of damage. And continually Flame Breath them as they follow you.

Ganking is one of Shyvana's weakest areas. She has no cc, but she is great at chasing down opponents. I often initiate with Dragon's Descent for the extra damage and so that I have AoE on all of her moves. If you are only ganking one person though it is best to just burnout in, Flame Breath them and exhaust them. I always keep Exhaust just for cc.
As for teamfights, with this build you are more of an AD carry and less of a tank. Keep this in mind and avoid rushing into the middle of a battle. Dragon form is great but also remember that you are a huge target. With Warmog's Armor and Atma's you should be able to survive most battles, but still avoid being focused. Be right behind the tank and if you start getting targeted dragon form so that you have the extra 25 armor/mr. Also with the amount of damaged stacked into this build if you can Flame Breath most of the enemy team and do a ton of damage with Burnout and double bite.

I haven't seen anyone do her items like this but I think it works best. If you have additional money at the end of the game (I always have tons left over) sell Atma's and buy a Bloodthirster. once you fill it, you will do extra damage and the lifesteal is pretty nice too. You will end up doing a lot of damage and killing squishies in a hit or two. Use Burnout and you can run through an entire team and kill the squishies in the back as long as they dont have CC.
With the 2 Phantom Dancers, Infinity Edge and Bloodthirster, you should be critting every single hit and doing about 900 a hit. This coupled with your attack speed and survivability is what makes this build dominate late game. Also the Bloodthirster will make you very survivable with the lifesteal.

There are some pretty good alternative items out there for Shyv.
: Adds some CC which she desperately needs. If you get this early game it will make your ganks way more successful. I wouldn't suggest it but you could potentially replace your Warmog's Armor with it. This would make her pretty glass tho, especially late game.
: Have an all AP enemy team? Shut them down with Force of Nature. You could replace one of the phantom Dancers with. If you have this and both phantom dancers then when you use burnout your speed will go up to 601. It's pretty fun running that fast.
: replace merc's treads with if you are against an enemy team with little or no CC.
: Same as force of nature if you find yourself too squishy. Keep in mind that Shyv can alternate between offense and defense. She is one of the best tanks and one of the best Carrys.
Again, sell Atma's and buy Bloodthirster if you can. This is usually only in an extremely long game.
: This is a great early game item. The active is wonderful and it gives gold. However late game replace it with a Phantom Dance.