This is my first guide, and I'm not the best at writing huge guides that fill you in on everything, but here is my take at Shyvana:

Shyvana is one of the fastest new junglers, able to level quicker than most due to Burnout and can usually take more damage than most like Nocturne. Though she lacks any hard CC (other than her ult's pullback) she has an amazing movement-speed steroid (Burnout) that also deals damage.

Using Twin Strike will be your main source of damage other than your auto attack. Shyvana's 'E' is a pretty useless ability, sure it lowers armour, but with runes it's pointless. I preferrably max out Twin Strike and Burnout alternately.

Pros:-Great Jungler
-Great Chaser
-Amazing at pushing, and knocking down turrets with her 'Q'
-Can take A LOT of damage
-Able to escape/chase over walls with Dragon's Descent

Cons:
-Has no hard CC
-Susceptible to any kind of hard CC used consequtively
-Able to be kited pretty easily, like a lighter, faster Nasus

Shyvana makes a great tank due to her Dragon's Descent giving her bonus armour and bonus effects on everything.

The reason I build a Bloodthister before FRATMOGS is because of how quickly Shyvana is able to stack up those counters. Shyvana is excellent at farming minion waves and jungle, and usually ends up being one of the richest champions in the game. Thus I go Bloodthirster because Twin Strike adds on-hit effects, granting double-lifesteal everytime you use it (with enough attack speed, you can use it every 2 seconds and steal about 250+ life each time).

The reason I go FRATMOGS is because of how ridiculously durable and inescapable it makes Shyvana (Atma's Impaler's armour bonus goes with the MR runes, making even more tanky without needing MR items) nearly unkillable with the combined lifesteal, hp, armour and mr in dragon form.