I know the popular way to play Shen is in the top lane, which is fantastic, but as a jungler he is one of my go-to champions. Whenever he isn't banned it's an all-but guaranteed win if played correctly in the jungle. He can't be denied or 2 v 1'd in the jungle as he can in top lane, and

his ult literally allows him to farm continuously

while at the same time maintaining map-wide pressure(though you can of course gank if other opportunities arise).

Understanding Shen will, simply put, boost your ELO.

Start Wolves then Blue Buff. Proceed to Wraiths, back to Wolves, then Red buff. Now is the time to decide if there's a gank opportunity. If not, go to Golemns, Wraiths, and Wolves then back. you should be able to get boots, Kindlegem, and a regrowth pendant which will go into your first item, Locket of the Iron Solari. From there, go back to Golems and proceed to clear camps until an opportunity arises to gank.

Try not to use Vorpal Blade as a finishing move, cause Getting at least 1 attack off on a target marked with Vorpal Blade will yeild greater regen.

I don't worry too much about monitoring dragon as Shen; If the enemy wants to do it, you can port in with your support/adc at any time (if they're dead you wouldn't be able to contest it anyways), or if you gank for a double-kill on bottom it's essentially a free dragon. Other than these opportunities, there's no point in stressing about it unless your team's really behind, in which case it's risky to try anyways.

In a fight,

don't start with a taunt unless the enemy ADC of squishy AP is in the front for some reason

Do, however, head in to the fight at the front of your team, aiming for the enemy squishies. If they aren't in range to taunt, they shouldn't be in range to be dealing damage to the rest of your team, so at that point you can turn around and help the bruisers/tanks which will inevitably be trying to kill your squishies. Marking one target with Vorpal Blade allows your squishies (ADC + AP) to focus on one person of your choosing and last longer in a fight. Always be threatening with your movement pattern to turn on the enemy ADC or AP with a taunt if they get too close. If you happen to extend too far from the rest of your team, you can ult back to your squishies and taunt the threats away from them in the middle of a teamfight if it's still up. Otherwise, head back and defend your squishies from the threats to them.

Your Jungle farming will turn into split-pushing in the latter half of the game, and you will usually ult into teamfights instead of initiating them as you would around dragon in the earlier half of the game. Aproach Baron the same way you'd approach dragon; take the opportunity if it presents itself but otherwise don't worry.

If you want to start a fight somewhere, make sure you ping so your team doesn't think you're just doing your own thing as many Shens do.

Split pushing will help if your behind, but if you're ahead you can usually just lead the charge on the enemy's base.