Now you may be wondering, why jungle shen? He's slow, and his ganks aren't the best, and he lacks damage. BUT when he hits 6, he can just farm the jungle all day, and still put pressure on all laners at all times. Also, when shen clears the jungle a few times, you will start to notice he develops basicly an infinite sustain jungle, and almost never needs to b if he is not disturbed.

Also, I prefer jungle shen over laning shen because if you ult to another lane as top lane shen, the enemy laner could push really hard and do quite a bit of damage to your tower.

The attack speed marks will help you clear the jungle faster, and will help you proc your passive more often.

The armor seals helps you survive in the jungle.

The mr per level glyphs give you some extra durability. Never bad to have extra resistances.

Movement speed quints are just good in general, helps you stick to a target.

Boots is obvious. Can get Ninja tabis or Mercury's Treads, doesn't really matter. Counter-pick.

Heart of Gold gives a nice amount of health, and some gp10 as shen can't really clear too fast, so he won't always have the highest income. Builds into Randuin's Omen later

Ionic Spark improves your jungle clear time, so pick this up as shen is slow as hell. The attack speed and health works well with your passive, while the aoe on-hit effect helps the jungle speed a lot

Aegis of the Legion is a nice aura item for your team. It gives mr, armor and health, with a bonus aura for more mr, armor and some extra damage. This item is really cheap for the stats it gives, so pick this up. Also helps when you ult to a teammate.

Phage will help you jungle better, improve your ganks with the additional slow, and will turn into a Frozen Mallet. If you are ahead, you can pick this up before aegis, or even skip this item and go for a warmogs instead, since you will have time to farm it up.

Force of Nature gives you some much needed mr. It also gives you movement speed, and health regen.

Obviously if you are really fed, you can pick up other and more luxurious items. This is just a general build, and you never have to follow it. The items are somewhat cheap for the most part, or build off of things you already get, so you won't have a bad transition into mid/late game unless you have been doing really bad, or counter jungled really hard

With this build, you will have decent attack speed to constantly apply Frozen Mallet and Ki Strike on the enemy team, and you'll be tanky and have Randuin's Omen active to for extra cc in teamfights.

You max q first for the sustain and damage it provides. E is next, as the extra damage helps with your ganking. You also get a lower cd on your dash. You rank up your ult whenever. You max your shield last, because the damage and sustain from q are needed, and the extra taunt duration is just better than some extra damage

You can pick up E at level 2 if you want to do a level 2 gank, or e at level 3 if you plan on ganking then.

For the jungle, you can start at blue or red if you want. You're teammates should always provide a leash, as there is nothing to lose from it, and you and your team only benefits from it.

If you are doing the blue route:
Start off at wolves. Get your teammates to help auto attack the wolves so they die faster, but make sure you take aggro, as leashing wolves will actually be slower. Make sure they don't take exp either.
Next, head over to blue, and have your mid lane leash the golem, and top or bot help damage the golem, depending on which side you are on. Smite the golem to secure the buff.
Next, clear wraiths, then wolves. After that, head over to red. By the time you get to red, your smite should be up. After clearing red, you can head to wraiths or twin golems, either does not matter. Following this route should get you to level 4.

The blue route is more for farming, and will be less riskier, as you have more energy regen to spam your q and w. It is a little bit slower, but you get your red buff near the end of your clear, and can gank afterwards.

If you are doing the red route
Get your teammates to leash wraiths, and damage it. After clearing, head to red. Get your teammates to leash and damage the lizard, and smite to secure the buff. Head over to twin golems, clear that, then clear wraiths, wolves, and finally blue. This route should get you to level 4.

The red route is more aggressive, and it is better to gank at level 2 or 3 instead of farming as you do not want to run out of your red buff. If you do use this for a standard clear, then red route is a bit faster, due to the damage on the buff, but you will be lower at level 4 then the blue route.

If you fear the enemy is going to invade you/your jungle.

If you think your enemy is going to steal one of your buffs, kill that buff/camp immediately, then pick up your other buff. This should get you to level 3, and it is advised that you immediately gank, as you have both buffs, and farming with them would be a waste.

If you think the enemy is going to steal your red, take wraiths and red, and immediately head over to blue and take that. Smite the red.

If you think the enemy is going to steal your blue, take wolves and blue, and immediately head over to red and take it. Smite blue.

If you think the enemy is going to try to start a level 1 teamfight, either gather your team, or go into their jungle and steal the buff the enemy is taking (usually blue)

If you are not planning on doing any early ganking, and just want to clear the jungle, here is a video to show the route if you do not understand. Play Video
In-depth video on jungle shen that stonewall008 made. Play Video
Btw, Shen is a ganking jungler until 6, as you can just farm when you have your ultimate, and still have a presence on all lanes, and if your teamates need help, you can countergank or gank with your ult.

In teamfights, you either want to try to taunt as many enemies, or enemy squishies, and when the taunt wears off, use your Randuin's Omen. Or, if you have somebody else to initiate in teamfights, then try to sit back and just protect your carries, and constantly apply the Frozen Mallet slow.

You can experiment with items, skill orders, jungle routes, and everything. You don't even have to follow this, or even read this at all. I leave the rest to you to figure out and discover what you prefer.