Your main goal is to clear all camps. Start by the adc/sup side, as it will help you to clear really quickler.
As soon as you hit lvl 6 you may start ganking.( If you see an opportunity to gank early dont be afraid to take it, her damage will still be massive)
Shyvana biggest trump is to farm really quickly. I usually am at highest lvl in the game. If you jungle right, you will get lvl 6 about 30-45 seconds before your top laner. Seize this opportunity to give a mass gank.
When ganking bot lane, shyvana's dragon's form allows her to deal a lot of damage to both bot enemies.

When ganking enemies your approach should be from behind them, this is because shyvana doesnt have a Stun or Slow ability.
If you have the info that the persn you are ganking doesnt have his flash, then try to ult them from behind.
She may not have a stun or slow, but she may be able to dive early in the game, this decision is yours to take. Remember her build allows her to have a big amount of health, and her ultimate is a gap closer and also gives her health.