Hopefully this guide taught the basics behind Shyvana and her build/playstyle as she is currently a very strong champion. Shyvana has fast clear time and huge mobility around the map as well as impressive dragon and buff control due to her having huge DPS against those targets with Twin bite. So hope you find her fun to play or dominate with her!

There are many routes with Shyvana you can do such as:

Standard to level 4:
Wolves->Blue->Wraiths->Double Golem->Red->Wraith

Standard level 3 gank top (often get a super leash/pull, aka dont smite first buff):
Wraiths->Red->Blue->Gank (blue side)
Wolves->Blue->Red->Gank (purple side)

Smite for obvious reasons, the choice between exhaust and flash depends on how you want to play the early game. Exhaust is often for a heavy gank style of play as Shyvana has no CC of her own and exhaust is a good CC to help in ganks as it slows them down (as well as being useful as a tank to weaken the opposing enemy's damage greatly).

Flash can be used as a 2nd summoner but often it's only used for excessive counterjungling as Shyvana wants to have an escape pre 6 in case the enemy surrounds her while shes taking the enemy buffs. Also can be useful later to get better positioning with her ult and to escape when her ult isn't up.

Shyvana has quickly moved up to one of the more viable junglers due to her extreme speed at moving around the map and clearing camps. This allows her to excel over slower junglers and be able to have a impact really early in the game and open up other uncommon possibilities such as counterjungling. Hopefully this guide will get you on the right track with where to start with her.