I don't like to ramble on, I like to be straight to the point. Hopefully you like my choices and if you have any tip's let me know.

Pros

Amazing damage
can attack large areas
can kill minions easily
you get to turn into a dragon
doesn't rely on mana

Cons

difficult to escape
targeted in groups
weak early game
killed easy by players with range

I like to focus on offense to make shyvanna deadly. Mess around and find what you like best. Really it all works just play around until you find a page you truly feel fits your play style.

I always start out with burnout. It helps you slay minions so you can level up faster. the next skill i like to level up is flame breath so you can shoot enemies that try to get away or hide in a bush when your weak and shoot from afar. level up the other skills however but just make sure you level up dragons decent as soon as your allowed too. dragons decent is the bread and butter of getting kills.

Passive: Fury of the Dragonborn

Also 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 15% of the ability's damage to debuffed targets.
Dragon's Descent - Attacks generate 2 Fury and Shyvana gains 1 Fury every 1.5 seconds while in human form.

I use teleport and revive because i want to get back into the action as quick as possible. Time is very valuable so its best not to waste it.