Shyvana is a meele campion. She can be played as full-tank, off-tank or on full-dps.
Shyvana is mostly played on top or in the jungle. I like it to play her on top because
of the fast and easy farming with Burnout and Flame Breath. If u push your lane always u can go for some farm in your jungle or you can go for counter jungling.

Skills:
Passiv = Dragonborn
Q = Twin Bite
W = Burnout
E = Flame Breath
R = Dragon's Descent

PROS:

- Great mobility
- High damage in any game phase
- Lots of AoE, specially in Dragon's Descent
- No mana
- Fast farming with " Burnout" and " Flame Breath"

CONS:

- No CC
- Hard vs ranged champs
- No strong ganker

With shyvana its always been the same summoner spells:

Flash for eacaping or engaging, like Flash -> Dragon's Descent + Twin Bite = last hit and kill ^^

or

Ghost can be used for faster helping on other lanes or chasing

Ignite for lowering health reg and killing low enemy champions

or

Exhaust because of no CC

or

Smite a must for faster junging in early and getting last hit on dragon and baron

For runes i have different choices :

Quintessence:

Greater Quintessence of Attack Damage for higher dmg output in early

Greater Quintessence of Health Extra health for more sustain

Greater Quintessence of Movement Speed I take them everytime because your faster then emenys with Boots if you use Burnout

Seals:

Greater Seal of Attack Speed for lower Twin Bite cd and faster farming

Greater Seal of Armor If you get an enemy ad-champion with a high dps in early

Glyphs:

Greater Glyph of Magic Resist If you are going tankier to resist vs AP users in early game

Greater Glyph of Scaling Magic Resist If you are going tankier to resist vs AP users

Greater Glyph of Attack Speed Same as the Seals, procs with passive and all skills

Marks:

Greater Mark of Attack Damage More AD means a stronger early game

Greater Mark of Attack Speed If you use Glyph as magic resist and Seals as armor

Full-Dps-Masteries:

Boots:

Berserker's Greaves I use them if i get a good feed in early

Mobility Boots if i jungle and i need to jungle on more lanes early and mid game

Mercury's Treads in late game everytime except a full AD-Based enemy team

Ninja Tabi on top vs AD-Champs

Dps items:

Spirit of the Elder Lizard I use it because its a passiv Red-Buff and its cheap

Blade of the Ruined King got a slow, IAS(Increst attack speed), lifesteal and dmg so what you need more

Last Whisper You can use it for more DPS with Twin Bite or Burnout

Frozen Mallet slow + hp = must on Shyvana

Maw of Malmortius good dmg and magic res and with the passiv you can survive a kartus ult

Ravenous Hydra one of the best items for shyvana

Black Cleaver can be usefull if you switch it for lizzard late game

Trinity Force im a fan of it because it pushes everything a bit and your Twin Bite gets an heavy dmg push with the passiv of Sheen but i wont play with it on shy its to expensive and the slow has only a chance of 25%

Zephyr i tried it but on shy you wont need much attack speed, the movement speed is a great buff and the tenacity if you wont build mercury treads

Infinity Edge yeah if you wanna try it i tried a full crit build on shy static shiv phantom dancer and infi and if it works and u get feeded, its amasing :P

Phantom Dancer crit isnt realy needed on shy but the IAS and movementspeed are good

Statikk Shiv only if i need to push hard on top like vs a ranged enemy champion

Wit's End the magic ress and the IAS are realy usefull but i think i play it only vs a full ap team

Sustain items:

Locket of the Iron Solari i think this isnt realy needed not for jungle and not for shy,
because the shield isnt realy good (230 at lvl 18), it blocks normaly only one normal attack

Randuin's Omen armor+hp+attack speed slow (if your focused) so only if your fed and the enemy got a good carry

Runic Bulwark realy good defensiv item because it pushes all but you or your support build it only, so let the support build it for that he/she isnt a one hit and spend the gold in other items

Shurelya's Battlesong strong item in mid game because of the 2-3 sec movementspeed for your team in chasing

Sunfire Aegis can be build if you need and only if u need more and more armor and hp.
But i think its no item for shy because you got Burnout and your Dragonborn

Warmog's Armor 1000 hp and good hpreg/5s so i bought it every game with shy(if their is a late game and the enemy wont surrender xD)

Zeke's Herald if the enemy team is feeded and you want to help out your team a bit with the 20 ad and 10% lifesteal aura. yes it can be build because its cheap

Atma's Impaler I build it only if i go for full tank because a bit dmg is needed everygame

Guardian Angel yeah what should i say the armor and magic res are good but the passiv,
i think normaly if you die while getting chased or in teamfight ,and your team start escaping ,all enemys will surround you and wait for your revive

Thornmail i build it sometimes to counter the enemys adc a bit

Zhonya's Hourglass the first time i tried it on shy was to funny i jumped in a 2vs5 with Dragon's Descent and used Burnout+ Zhonya's Hourglass and the enemy team all stay there and think *hmmmm, wtf, why, how, holy ***** and i *yeah its a hourglass and i used it *.
So its for some funny moments ingame ^^

First of all i play an aggressiv jungle/counter jungle because of Shyvana's movementspeed and farmspeed
1. I start with stealing red/blue or my team want to invade.
2. As fast as i can i`ll get my blue or red (depending on what i got).
Sometimes if i got the enemys blue, my red and my blue is already up ill let my apc take it(or adc red).
3. Search for a gankable lane if their no go ahead jungling with wraiths
4. Golems for lvl 4 or 5 if u ganked and killed an enemy.
5. Yeah i know i wanna go for another gank but first of all i need hp and maybe boots and 1-2wards for counter jungling
6. I ward the enemy jungle at the marked spots

P.s Search everytime for gankable lanes and use smite as often as u can except its time for drag/baron then save it