Even though this guide was just made, I made a bunch of adjustments to how I play Shyvana contrary to what this guide states. I will redo this guide within the next few days and post my new build, as my results with the new build completely surpass what I've been doing earlier.

Pros

-Higher survivability
-Strong damage potential
-Able to quickly escape if need be
-She's a dragon, come on

Cons

-Lower attack speed than other builds
-Low ability power
-Susceptible to CC
-Fairly difficult to master

As most of you are aware, Shyvana was only released yesterday (at the time of writing this guide) and there exists a ton of different paths you can choose to take her in regard to builds. I've tried a few different builds on here as well as those through my own accord through both AI battles and player matches. This guide here is a result of my most optimal set-up so far that has resulted in a devastating build for Shyvana. For this build you will mostly be relying on runes for attack speed, and her items for attack damage and defensive stats. By the time endgame comes with this item set up you will not need any additional attack speed as you will tear through enemies in seconds and retain enough speed potential that you will remain in dragon form long enough to take care of team fights.

Greater Mark of Desolation
Armor penetration is great for Shyvana, so 9 of these should be default.

Greater Seal of Attack Speed
Since this build lacks in much-needed attack speed, I strongly recommend putting in attack speed seals. Attack speed is, in essence, Shyvana's most important stat (although you don't need to go overboard on it).

Greater Glyph of Scaling Magic Resist
You can either toss in these for some extra magic resist (therefore, survivability) or place in some more attack speed runes. This is up to you. If you play Shyvana well enough, you probably won't need the additional attack speed if you feed on enemies enough for gold. These runes just make you a bit tougher to beat.

Greater Quintessence of Attack Speed
More attack speed. Always fun.

Great:

Ghost: Probably the most important spell for Shyvana during all points of the game. At the beginning it is especially important because if you're following this build you will not have boots until after you purchase Wit's End. Ghost + Burnout makes you especially mobile, and it's also useful for chasing down enemies as a dragon before your Fury runs out.

Flash: Useful for getting out of hairy situations, which is very common early game considering how squishy you are before level 6.

Ignite: Why not add fire to fire? Makes you deadlier during early game and can help pull off some early kills.

Exhaust: Good for escaping a gank (or doing a gank for that matter). Adds more survivability for early game.

Mediocre:

Heal: Can be useful before level 6, but for the rest of the game it'll be almost worthless.

Smite: Useful if you're jungling, but that's all.

Cleanse: Good for team fights when you'll probably be CC'd to death when they see a giant dragon coming at them, but that's about it.

Teleport: Can be useful for getting around the map quickly, especially if you end up dying a lot for some reason.

Bad:

Revive: Never. Point of playing a dragon is to be scary and relentless, not to be slain repeatedly.

Clarity: If you play Shyvana and I have to explain this one to you you should not be playing Shyvana.

For items I open up with a bit of magic resist and go straight for Wit's End as it provides a good deal of initial attack speed, plus the passive on it makes you all the more deadly. I don't worry about boots right at the beginning because with Ghost and Burnout, Shyvana is already fairly mobile early game. Use Burnout while moving from location to location for a quick movement speed buff. When it actually is time to get boots after obtaining Wit's End, I recommend Berserker's Greaves for the additional attack speed to make up for the rest of the build.

Shyvana is fairly intimidating to use at first because of her hybrid capabilities, but as you may have noticed so far the build is relying on attack as opposed to her abilities. Getting Frozen Mallet makes it a lot easier to rack in kills through slowing down your enemies, and the additional health adds to survivability. Enemies will have trouble escaping your dragon form with this item, and they'd be stupid to attempt to fight back (unless they're already a lot more fed than you are, which is hopefully not the case).

The last part of the build is up to you, as some might prefer lifesteal items such as Hextech Gunblade which is also good (plus it adds to your ability power, making your spells not as weak). I chose to instead use Atma's Impaler, Youmuu's Ghostblade, and Warmog's Armor. With Atma's Impaler and the Warmog's Armor, not only will you have increased survivability, but your damage will significantly increase as well. Youmuu's Ghostblade is great for high damage potential, and using its active will help you stay in dragon form longer (or ensuring that a difficult enemy will succumb to your claws). Ultimately, it is up to you what type of build you end up taking (especially if you prefer lifesteal), but I'd strongly recommend giving this one a try as enemies will have a hard time killing you, but you will have a field day killing them.

Fury of the Dragonborn
Your passive ability. All basic attacks do the following to your abilities:
-Twin Bite: Reduces its cooldown by 0.5 seconds.
-Burnout: Extends the duration by 1 second to a maximum of 6 seconds.
-Flame Breath: Deals 15% of the ability's damage to debuffed targets.
-Dragon's Descent: Attacks generate 2 Fury and Shyvana passively gains Fury over time while in human form.

Twin Bite
Q. Your most important attack with this build. This attack is increased based on your physical attack power, and it allows you to quickly mow down a target. The more you land a basic attack, the shorter the cooldown of this ability is. One of the main reasons why having a high attack speed is important. You will want to give this ability the highest priority for leveling up.

Dragon Form: Cleaves all enemies in front of you, dealing large amounts of damage.

Burnout
W. Your second-most important ability. Burnout causes damage to all enemies around you, which makes you more intimidating to enemy melee. Not only that, but it makes you move around a lot faster. Since you don't have mana on Shyvana, use this as often as possible, especially if you end up getting killed and need to run back to your spot.

Dragon Form: Scorches the earth everywhere you walk while this is active, causing damage to all enemies standing in its field. If you cast this before launching at your enemy as a dragon, you will leave a large trail of fire behind you.

Flame Breath
E. This will be one of your weaker abilities with this build; however, it is not useless. First of all, I strongly recommend setting a smart cast shortcut to use this as opposed to selecting a direction and firing. I set my smart cast to C for this ability (the same for Cassiopeia's Twin Fang), so I can quickly launch a fireball in the direction of my mouse cursor when it is off cooldown. This can be used for mowing down minions faster and getting last kills or for harassing enemies. The main thing for this ability is to use it on a player you are about to go medieval on (medieval, dragons, get it? ... ok) as it lowers their armor rating, making them easier to kill.

Dragon Form: Conflagurates all enemies in a cone before you with a wave of fire.

Dragon's Descent
R. Your ultimate. This is where Shyvana really shines. Press R and select a nearby destination to launch yourself as a flaming dragon and take all enemies with you. As a dragon you gain increased stats and all of your abilities are improved. If your enemies are smart, they will run away (or try to), but if you follow this build they probably won't have the chance. Your Fury gauge will deplete while you're in dragon form, but each physical attack will allow you to remain a dragon, which makes attack speed pretty important. This ability is also great if you need to escape quickly, as launching yourself as a dragon lets you move across the map very fast and gives you added survivability. Toss a Burnout with that too and no one will be able to catch you even in their wildest dreams.

Passively, this ability significantly increases your armor and magic resistance (even moreso in dragon form).

This guide will probably remain under construction for a while after coming across any significant weaknesses (or finding vast improvements). Since this is a new character, this is by no means a finished masterpiece of a guide since everyone including me is still trying this character out. I decided to make this character my main because for one I'm a big fan of dragons and for two I love her aggressive and unyielding playstyle.

Leave any constructive comments you may have about this guide and share your opinions, as I like trying different things out. If this guide worked for you, great, let me know.