I am what you would call a newb to LoL. I enjoy playing the game, but also hate it at times due to AFK's and feeders. And yes because I am a newb, sometimes I feed unintentionally, however I do my best not to feed. After all, no one play's LoL to feed on purpose, at least that's the idea but I swear sometimes people do feed on purpose for the hell of it and to make my experience miserable.
I have read several guides and have found them to be good, but this is my take on Shyvana and the way I like to play her. I enjoy the shear tank she has in her compared to other champs I have played. I have found myself just laughing as the entire opposing team tries to kill me and it takes a five or more seconds for them to kill me. Not only that but because she does damage very well with her W, she can easily focus a squishy and take one or two with her if all goes to hell in a handbasket.
I currently main her as my Jungle, and try to play her when ever possible. I have found very little resistance when facing other junglers, most junglers avoid me where possible, but I have had a few try to gank me counter jungling and I have sent them packing.
Anyway read it, don't read it, take this guide with a grain of salt. It's just the way I play her :)
Creeping / Jungling
Now you would think that Shyvana would not need blue to jungle, and well, she doesn't. But this is the route I take when jungling. I start at Blue, now people have asked me why do I start at blue. And I always had difficulty explaining it, then it hit me. The reason I go for Blue first is because Shyvana needs Red to gank. If I get red first I waste most of it jungling, and well Shyvana needs red to gank effectively. So I get blue first, followed by Wolves, then straight to Red. If done correctly you will be half way to lvl 3 at the end of Red, get to lvl 3 and gank if possible.
You can skip the 2nd blue if your mid needs it and give it to them, if you have a mid, like Yasuo, take blue for XP/Gold.
Other than that its a standard jungle route. I won't go into great detail just yet, because there are better guides out there for the routes to take etc ... I may expand in future.