Half-Dragons are the forbidden scions of humans and shape-shifting dragons. There have been few in the world, as they are typically hunted down by their draconian relatives. The scarce and reclusive dragons left on Runeterra find it disgusting to mix their blood with the frivolous and violent lesser races. However, there are those who become fascinated with humans, such as Shyvana's father. It was to Prince Jarvan IV's surprise when his hunt led him to a legendary young half-dragon. She wept over the dead, mutilated corpse of her father, murdered for her existence. Something in Jarvan was moved by Shyvana's plight. Together they plotted revenge against the mighty dragon resposible. The assault cost the Demacian Prince many men, and nearly his life, but ultimately Shyvana and he prevailed.

The experience changed the both of them. Shyvana lost her place in the world, left alone to be hunted by those dragons who discovered her existence. Because of what he'd seen, Jarvan lost his taste for the hunt and wished to return home as protector of his people. Jarvan IV, as Crown Prince of Demacia, offered Shyvana a place as a noble warrior in the ranks of the elite guard. Out of gratitude and necessity, she accepted. Since their return to Demacia, Shyvana has proven herself to be a fierce and powerful soldier. She blends her fiery draconian blood with her adopted principles of justice. She revels in the power she now feels in the human world and there are few who do not quake before her in combat. However, by and large there remains only one place for glorious battle. When Jarvan joined the League of Legends, it wasn't long before Shyvana answered the call as well.

Self explanatory. Your Armour penetration for damage, and flat armour/magic per level for sustain.

9 in offence for your damage, and defense tree for sustain. Shhyvana does not have great sustain until she gets her wriggles and easily kited so having defense is impor

Defensive start with the 5 potions. This should allow you to solo top until you are able to afford wriggles, or maybe a vampiric spectre and boots.

Wriggles-Has everything you need
Boots-Ninja tabi if they are AD heavy, merc treads if they are CC, or AP heavy.
Phage-The early slow and hp, makes you harder to kite with the slow
Wit's End-Just works really well, attack speed, damage, magic resist.
Atmas Impaler-you should have alot of HP, atmas is great choice, for the armour/crit.
frozen-works well with atmas and makes you meaty.

Last item is situational, extra DPS, tankiness, warmogs even. Normally games don't last this long.

Land you "e" > Burnout > Auto > Q...

if they fight, and you are winning continue.

if they fight, and you are losing... retreat. durr.

if they run, chase normally without dragon, unless you can kill. Simple.

Note: never use dragon to initiate. It's really bad. Using it after initiation and screwing up their teams positioning is best.