Because Shyvana has no "life get", she either relies on taking camps fast/not taking a lot of damage, Vampiric Scepter, or pots. Because Shyvana has no armor ability as well, the best first item would be cloth armor (and 5 pots). After that you don't want to waste any more money on pots, therefore you have to get Vampiric Scepter. Next would come razors (you don't speed as your w already covers it). Then would be the usual jungler boots, a money item (since you're going to build off it), then Wriggle's.
When ganking, you want to start off with w and do a "double-tap"with your q, making your w last longer, you may want to use your exhaust early as you have no speed.