So! You decided to pick Shyvana and for some weird reason, to read this guide. Cannot actually blame you for that, since I wasted time to write it.
Let me put few pointers, what I will speak about:
1. Why should you play Shyvana at all
2. Summoner Spells
3. Runes
4. Basic builds
5. Some possible match-ups
6. Masteries

While the title is Pros / Cons its more about why should you pick Shyvana at all.
Most of you are probably used to table with few pointers about pros and cons, sorry I will not do it, since its important to actually read it. Shyvana is heavy and powerful tank/off-tank, depends on build. She has potential to deal huge amount of damage without building AD or ATS (attack speed, for people who do not know). She also possess natural tank since her passive grants you armor and magic resist Dragonborn. On the other hand she has no slows, stuns or good cc (crowd control). With only her ultimate to provide her distraction, with knock back, it might prove hard to fit her with every team composition. You might find yourself saving enemies from hard cc, like Glacial Prison or Curse of the Sad Mummy. That being said, you can for sure also push someone IN some skills, like Crowstorm.
All said and done, its mostly skill dependent, which mean you will be dead-weight or great teammate.

Short chapter, not much you can write about it.
Teleport
Flash
Ghost
Smite
Find the best combination for yourself and be happy with it.

Ok, that part is trickier. I just found that list which should contain runes have items instead, so I am gonna just write about them, deal with it.
Runes to consider:
-Attack damage
-Attack speed
-Cooldown reduction
-Armor
-Mres
-Lifesteal
-Health regeneration
-Movement Speed
Attack damage, attack speed and cdr (cooldown reduction), are offensive runes.
Attack damage is better vs squishier targets, while attack speed is way better against tanks, since you will deal most of damage using Flame Breath, since % dmg is plainly awesome.
Armor and mres is self explanatory. One note, its actually better to make at least 2 rune sets instead of combining both mres and armor.
Movement speed, Health regen and lifesteal.
Usually I personally use lifesteal, since its better in lategame than health regen and its easier to lane with it than with movement speed. Though all of them have their uses.
Health regeneration is something to consider while fighting ranged champions, since you will not be able to attack as much to heal up with lifesteal and movement speed is plainly useful while facing enemies that might kite you.

I made few example sets at build tab. You for sure noticed they are more or less similar. While most of the items do not exactly need explanation, some do. All 3 builds are heavier on hp than resistances. The reason is simple, but easy to miss. Dragonborn grants you some mres and armor and the values double while in dragon form. For that reason you will have greater benefit from hp than armor and mres. Worth mentioning is the fact, that Frozen Mallet is basically a must if you face running heroes like Udyr, Gnar etc. I usually take it instead of Warmog's Armor.
Blade of the Ruined King, I placed it in 2/3 exemplar builds, but its worth to consider Guinsoo's Rageblade too since it doubles on hit damage from . I do not think there is definite answer for the question which is better, but Blade of the Ruined King grants you mov speed and hp steal on active, for that reason I prefer it.
Phantom Dancer. Something most do not consider, yet so amazing item especially on Miss Dragonborn. Shyvana benefits greatly from attack speed, and that babe grants a lot of it, flat movement speed, critical strike which can be more or less disregarded and two passives.
One makes you capable of chasing the enemies with extreme ease and the second one makes dueling monster. While 12% damage reduction from target is not much for squishy adc, for heavy tank with tons of HP its ridiculous, enemies barely scratch you anyway and this sweetheart reduce that damage even further.

At this section I would like to just write that I placed few enemies to give you an idea what is and what is not troublesome to fight against.
For that reason, you might notice its easier to fight with enemies that you can take on face to face, close and personal. On the other hand she struggles with champions that can heavily harass her and put in cc.

I decided to add this chapter after some deep thinking. I thought explaining them might be nice, be proud of me. Usually for tanky champions as Shyvana you would consider taking Grasp of the Undying. In most cases I would agree, but not here. Fervor of Battle is better for Shyvana in almost all cases. The reasoning behind it is very simple. Shyvana deals damage very frequently and from many sources. Burnout, Twin Bite, Flame Breath, Dragon's Descent, auto attack, each and every time one of those deal damage to your opponent you gain stack. As you deal that damage few times per second, the amount of stacks will skyrocket from 0 to max in no time and in practice greatly increase your damage especially, since you are gonna invest more into attack speed than attack damage.

Complete summary: I do not even know why did I write it. But it is done and I hope it will prove useful for someone. Thank you for reading and I am always open for suggestions.