Greetings everyone.
This guide is not really a guide, but my way of playing Shyvana.
I am of course open to any kind of suggestions so please don't hold back.

There's quite a lot of different rune choices for Shyvana.
I've been running mostly with Greater Mark of Desolation, Greater Seal of Resilience and Greater Glyph Shielding.
If you prefer attack speed you can use those instead.
For quintessence there's the choice of attack speed, armor penetration or health (or a mixture of them).
You may be thinking; "why choose armor penetration if 3 of her 4 abilites deal magic damage". Because Shyvana is a lot about auto-attacking (because of her passive).

I've gone with a 22/0/8 mastery. I like the offensive ones but I also make sure to pick Archaic Knowledge because, as mentioned, 3 of Shyvana's 4 abilites deal magic damage.
I choose not to take Utility Mastery because I think there are plenty of other champions who can use the buffs more than Shyvana, but feel free to take it if you want.

I've chosen to start with a Doran's Shield but Doran's Blade can be chosen as well, or you could just start with Boots of Speed and 3 pots if you want to get into the build quickly.

For the 6th item, there's a number of choices. You can choose a Force of Nature if they're very AP heavy and you need more magic resist. You can also make some lifesteal through Bloodthirster or even Hextech Gunblade (haven't tested it though). If you want more damage through Atma's you can make a Warmog's Armor.

Will add more to the guide later.