Hello, and welcome to my guide on playing the solo top lane as Shyvana.
I have played Shyvana many a time, and believe that this build works exceedingly well when playing her in such a fashion.
She excels solo top, and this guide aims to show how to do so effectively.

Twin Bite: This essentially does extra damage on the next hit. When in dragon form, this damages in an area in front of you. You typically want to use this third in a fight.

Burnout: This is AOE damage, and speeds you up. Use this when escaping, catching up to people, farming and also in team fights. When in dragon form, this leaves a trail of flames. Use this ability first in a fight.

Flame Breath: This does damage, plus reduces armor. When in dragon form, this deals damage in a cone. Use this second in a fight to ensure maximum damage output.

Dragons Descent: You fly towards target location as a dragon (pushing people back; this allows you to push people around and use this to your advantage.) This gives you increased stats also, and your abilities have extra effects. Use this when you want to engage in a team fight, when you want to ensure a one on one kill, or to escape over walls.

These runes are pretty standard; giving you the health, magic resist, armor and armor penetration that is required to deal a fairly substantial amount of damage, whilst still being resilient to ganks.

Once again, these are pretty standard masteries. The increased AD, AS, Life Steal and ArPen are extremely potent against most champions in the solo top.
The increased gold gain in the Utility tree enables you to get the items that you really need as quick as possible, to be able to push your lane and then assist other lanes.
The increased experience enables you to keep up with other lanes if you are against a particularly tricky opponent, but also allows you to constantly stay at the highest level in the game.
The increased movement speed is also incredibly handy, as when coupled with Burnout, Ghost and Exhaust, lets you secure a kill when your friendly jungler ganks your lane.

Doran's Shield is, in my opinion, the best starting item for Shyvana as the increased and health regen lets you stay in lane and farm as much as possible.

The next purchase is Madreds Razor, as the passive allows even more potent farming. Also, the armor lets you stay in lane for much longer.

Next item purchase is main boots. You can choose one of two boots for this. If the enemy solo top has a lot of magic damage and stuns, then Mercury Treads are the way to go. Otherwise, go straight for the Beserker's Greaves as you can lay down as much damage as possible when attacking the enemy, plus you can again farm extremely well.

Next, turn the Madreds into a Wriggles Lantern. Wriggles lantern is very good as it retains the passive from Madreds Razor, plus it gives lifesteal. This, again, enables you to lane for longer but it also allows you to become a much more effective one on one champion.
ALWAYS remember to place the free ward from it in the river bush, to help your fellow jungler and to stop ganks in your lane.

The next two main purchases are Warmogs Armor then Atmas Impaler. These both combine to give you incredible health/ health regen, but also insane armor AND attack damage. By now, you will be resilient enough to save yourself from any gank plus help almost anywhere in the game.

From here on, you can typically choose any items that you wish, depending on the team. If they are very heavy AP, then invest in a Force of Nature for the high magic resist and health regen. If they have a more balanced damage team, then invest in the Wits End for both the magic resist and passive which enables you to deal more damage, plus it ties in with your attack speed to ensure a high magic resist all around.

The Frozen Mallet will give you even more attack damage (both from its base stats and the passive of Atma's Impaler) plus health and the ability to slow. This is useful as it means that the enemy champions are more likely to stay in your Burnout AOE.

If the enemy has a lot of AD power, then invest in a Thormail to ensure that they wont be as much of a threat.
Otherwise, get a Sunfire Cape as the health will again give increased AD with Atma's Impaler, the armor will be useful for obvious reasons and the passive will work well with your Burnout AOE.

You typically want to max your Burnout first, as this enables efficient farming, plus power out put against enemy champions. It also gives a significant speed boost, which allows you to escape from almost any gank.

Next you want to max out Twin Bite, as it allows for even better farming, and also deals significant damage to turrets AND champions.

Max Flame Breath last and take your Ult when possible.

I usually take exhaust as it allows my jungler to gank extremely well, plus it ensures that the enemy that I am nuking down cannot turn around and take me down, and it keeps them in range of my AOE.

Ghost works well also on Shyvana as it means that I can escape from almost anything when coupled with Burnout and I can also catch up with enemys effectively.

Pro's of Shyvana:
-Extremely good at escaping
-Very tanky whilst also dealing a lot of damage
-Can single out targets.
-Decent CC with Ult.

Con's:
-Not the best early game
-Can be hard to lane against a ranged champion
-All abilities attack in front of you (apart from Burnout) so she is relatively positional.

So this has been my Shyvana build guide. Hope it works well for you, as it sure works very well for me.
Thanks.
Summoner name: Fuzzy Redemption