Welcome to my Shyvana jungling guide.
This is my first guide, so please feel free to comment and make any suggestions. First of all I'm sorry for all my grammar mistakes but english is not my native language ;) I played Shyvana since day 1 and jungled her all the time, I tried several builds and like this one the most. It's fun to play, it makes you very viable in teamfights but also lets you 1v1 pretty much everybody.
Hope you'll enjoy it.

Pros:
-One of the best farmers and junglers in game (imho)
-With this build you get sick splash damage
-Fun to play
-One of the fastest junglers
-Awesome team fighter
-Awesome ganker/1v1
-She's a dragon :)
-No real counter
Cons:
-Squishy early game
-Shows her real power late game
-Item dependant (but that's not a problem since she farms like a boss and ganking after you get to lvl 6 is pretty easy)
-She lacks CC/slow/gap closer(besides her ult) but that's what exhaust's for.

I'm using attack speed runes, because it's making the jungling easier and extends the duration of your ultimate. Armor runes also make the jungling easier, and reduce your squishyness early game.

Abilities:

Twin Bite
Shyvana strikes twice on her next attack. Both attacks trigger On-Hit effects and Fury of the Dragonborn effects.
Dragon Form: Twin Bite cleaves all units in front of Shyvana.

Burnout
Shyvana deals magic damage per second to nearby enemies and her Movement Speed is greatly increased for 3 seconds. Shyvana's Movement Speed bonus is reduced over time.
Dragon Form: Burnout scorches the earth, continuing to damage enemies that stand on it.

Flame Breath
Shyvana unleashes a fireball that deals magic damage and melts the target's Armor for 4 seconds.
Dragon Form: Flame Breath engulfs all units in a cone in front of Shyvana.

Dragon's Descent (Ultimate)
Active: Shyvana transforms into a dragon and takes flight to a target location. Enemies along her path take magic damage and are knocked toward her target location.
Passive: Shyvana reinforces her scales, increasing her Armor and Magic Resist. Defensive bonuses are doubled in Dragon Form.

Fury of the Dragonborn (Passive)
Shyvana's melee attacks enhance her abilities.
Twin Bite - Reduces the cooldown by 0.5 seconds.
Burnout - Extends the duration by 1 second to a maximum of 6 seconds.
Flame Breath - Deals 20% 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.

Maxing your W (Burnout) is a priority because it's necessary for jungling. Q (Twin Bite) is second in priority. Of course R(Dragon's Descent) is above all. Max your E(Flame Breath) last, but get it at lvl 4 because it lowers enemy armor.

The basic sequence is E->W->Q->R->Q->W->Q->E

It changes depending on the situation. I like to save the ult in case somebody runs away harras enemies with WQE and when you're certain, go for the kill with R
When your ganking and have your allies nearby initiating with R is really nice. You just have to get a feel of her and you'll know what to do.

Before everybody will start to troll, I know Tiamat's got mana regen but it's a really nice item for her.
Shyvana's Twin Bite(Q) recieves the apply on hit buffs.
So when you use Burnout(W) you get the buff from Sheen and Tiamat's splash bonus which comes in handy in the teamfights or farming and it does really nice damage, not mentioning that when you ult your Twin Bite(Q) damages all enemies in front of you so it's some insane splash damage we're talking about. Wriggle's Lantern is an obvious choice, makes jungling safer and easier, same goes for farming. Trinity Force is a nice item too cause it holds Sheens buff enhances your survivalability, again it does add mana but still it's a nice item to have because of its other benefits. Warmog's Armor further increases survivalability and at that point you're pretty unstoppable. Atma's Impaler is an obvious choice with Warmog's. Now in the end it's a matter of taste whether you will pick the Hextech Gunblade or the Bloodthirster. Both items are good for her but at this point in game I'd say Gunblade's better. You can change Berserker's Greaves for Boots of Lucidity or Mercury TreadsMerc Treads depending on your taste :)

Creep sequence:
Wolves
Wraiths(smite the blue wraith)
Double Golems
Base
Blue Buff
Wolves
Wraiths
Double Golems
Base
Red Buff
and so on (Remember to gank of course :) )

Creep sequence is in this video Play Video
It's very important that you always use your Q(Twin Bite) when W(Burnout) is activated because it esxtends the duration of Burnout, so to maximize damage use it as often as you can. Also Twin Bite doesn't reset the autoattack like for instance Nasus's q does, so use it after you attack to maximize the damage output. Ganking isn't very effective till level 6, but you still can pack a nice punch if your teammates are good. Shyvana's also a pretty good counter jungler because she gets the buffs earlier than others, so you might catch the other jungle in his territory with low health and easily kill him.
Remember to have your runes, otherwise it's hard to jungle with Shyvana.

Shyvana is one of the most fun to play champs I have played. If you change your masteries, runes and summoner spells a bit and change Wriggle's Lantern for Doran's Blade you can use this build to lane normally. Hope you enjoyed it!