Personally,I like to start of with the red buff,because I find it more useful than the blue buff for Shyvana,I do not like to take wraiths 1st nor wolves..
Shyvana is a super fast jungler,you can also take exhaust and smite as your summoner spells,but if you took flash,take Phage ASAP.

Shyvana has a pretty hard time ganking if the target hasn't pushed very much cause of lack of cc,which is why again I recommend exhaust or an early Phage..

Shyvana is kind of a teamfight leader,her ultimate is so useful for engaging,infact I recommend focusing your ultimate on a carry to fly towards him.

These items aren't in the item list,but very good to take:
Ionic Spark
Maw of Malmortius
Yomumu's Ghostblade
Ninja Tabi
Heart of gold (If you're taking it I recommend before taking the wriggles-or instead of wriggles).

If you get confused trying to figure smth out here,I'm sorry it's my 1st guide I'm still getting used to everything.