I'm going to share with everyone the best Shyvana build out in the game right now.

I use 3AS and 6Arm pen marks, 9Armor seals, 9MR per level glyphs, and 3Flat AD quints.

I find these to be really useful especially when jungling. The attack speed allows you to still have the attack speed Shyvana really thrives on(not to mention it amplifies your attack animations.)

The Armor pen marks I find quite useful, because it allows you to clear the jungle that much faster with your W. Not to mention 6 of them are equal to 3 Armor Pen Quints.

The Seals and Glyphs are standard.

The Quints are nice because Shyvana's W and Q scales of AD and along with the AS and ArP the Jungle clearing and the damage output is just so high.

Take 9/21/0 Masteries on Shyvana.
Take 1 point on Summoner's Wrath( for exhaust), 3 on Brute Force, 4 on Sorcery, and 1 on Arcane Knowledge.
Now you might be wondering why Arcane Knowledge and Sorcery instead of Alacrity and Weapons Expertise. The reasons for that are 1 CDR, and 2 if you look closely all of Shyvana's damage output (except her Q) is magic damage. Her W, E, Q are all magic damage, and it really allows you to get fed early.

21 Points on Defense are standard for jungling of course.
1 point for smite, 3 on armor, take everything for less damage (yes indomitable and the other thing EVEN THE 6 DAMAGE THE MINIONS.) Take the health, and also the HP Regen (Shyvana has no early sustain so IT'S VERY USEFUL.) Movement Speed/CDR Per Level and lastly Juggernaut.

Skill sequence you take your ulti whenever you can. Max your W first ALWAYS. Q second because you have twice the chance to proc wriggles,phage,red, ETC...

Just Follow those items on the list, BUT the Wit's can be changed to Madred's Bloodrazor (depending on the enemy team) and you can also change mallet to tri force (again depending on what your team needs/counter enemy team.)

I get a maw of malmortius if they're AP heavy and actually an atmas if they're AD heavy. GA is also nice if you need it.

BUY WARDS WHENEVER YOU CAN!

Smite/Exhaust = MONSTER ON SHYVANA

Smite/Flash = Okay and allows you to make plays (if you/'re skilled enough)

You're first to dive in and Pop your randuins. try to get the AD carry and make sure yours is protected as well.

If you can play shyvana right you should be able to win your games easily. She's such a strong champion, and her engage with the randuins is a monster. She lacks CC (which is why you get randuins and frozen mallet.) Try to stay clear of getting kited, unless you have your W don't chase the ADC (never chase without ward coverage though!)