Before you jungle Shyvana, you should know here pros and cons

Pros
+She is an aoe jungler, and her w can clear waves like a boss.
+She is the one of the fastest gankers and can get into position quickly.
+She is a fairly easy jungler as long as you max your w.
+She is a very good chaser especially if you have a slow (red or frozen mallet)
+She is an excellent initiator with her ultimate and can nuke the ad or ap carry.
+Her e and her q work well while going 1v1, and can put out a surprising amount of burst.

Cons

-Early game she has no cc, so a gank needs to be set up correctly
-She needs her team in an initiation, so be sure that your team will follow you after an ultimate.
-Your ult goes off fury, and this can take a while to accumulate. Do not get pinned without your ultimate.
-Her ultimate is very hard to land, especially when initiating away from your team.

For runing shyvana, I just use standard jungling runes. Armor yellows for the early jungling strength, armor pen reds, and attack speed quints. For your blues, it is not a bad idea to use flat CDR, as this will allow you to spam your w early game more, as well as use your E/Q combo on the larger minions. Blues is more player preference however, and depends on the type of jungler you want to be.
Attack speed will give you better early game minion clearing, but I am only using these because they are standard and I have not tested CDR runes yet.

There are one of a few ways to jungle shyvana. I find that the most successful junglers are the ones that gank early and often, but a conservative jungler with good ganks can also be a good thing.

Path 1
-Start at red after having a teammate leash.
-Gank mid at lvl 2 and flash if necessary to get a kill, if not, force the mid lane to B.
-Go for wraiths using Q on the big wraith.
-Go for golems, smiting the big one.
(Back) Go back to buy cloth armor/wards if necessary
-Either give blue to the mid lane, or take it.
-Go for wolves
-Clear wraiths
-Clear Golems
-Buy madreds and wriggles early on, it will massively help with jungling, and make an early dragon extremely viable.

The core items you NEED early game for jungling / ganking are:
-Wriggles Lantern: This item provides early tankiness, as well as map awareness with free wards

-Merc treads: Especially helpful for ganking players with cc, and a MUST for every teamfight and initiation.

-Wits end is excellent to give shyvana early game mass damage and balance magic resist with armor.

After you have built these core items the rest can be up to the enemy team comp, but I highly recommend frozen mallet and /or frozen heart. An optional early glacial shroud will help to max your CDR, which is extremely helpful with shyvana.

When ganking it is very important to either:
Note:
Before level 6, it is VERY IMPORTANT that you gank with red or have teammates put down hard cc. Without this you will not be able to keep your enemmy slowed enough to kill them, because of shyvana's lack of early game cc.

After level 6:
Initiate with Dragon's Descent (your ultimate) to push the enemy back into your teammate
or - -
Come from behind with your w activated whenever possible and provide some massive damage.

Ganking mid:
If mid lane is pushed, ganking will be very easy. If it is not, flash + Dragon's Descent can be extremely useful or just come in with w activated from behind the enemy. Gank mid early and often to shut down mid lane and allow your teammates to outfarm the enemy.

Ganking bot:
It is extremely important that when you gank bot, you land your E on one of the enemy laners, and then follow up with a Q and W active. Dragon's Descent will easily get two kills if you are positioned correctly.

Ganking top:
When ganking top be SURE to land your E. Without it, you may not have enough damage output with your teammate to kill the enemy champion.

Shyvana is one of the best initiators, and you should almost always be the first in a teamfight with your Dragon's descent. If possible, target the AD or AP carry. With the bonus armor and MR you get from your ultimate, it should be no problem tanking damage while targeting the carries. However, it is VERY important you make sure your team will follow you. I have seen too many times Shyvanas initiate and the team not follow. While in a teamfight, activate your W to do AOE damage, and use your E as much as possible to shred armor combined with your Q.