New Gen Shen plays like a lot different Tank. If you look into his base stats, you will notice they are beyond awful. I believe it was 73 health per level and 2.5 armor per level now.
However, Shen has two active mitigation spells, being his Passive and W. These are what make him a Tank and should be what you use whenever they will mitigate damage.
Laning Phase
In lane, it is important to not use your Q to CS unless you are alone in lane. You have to become really good at seeing what your enemy plans to do based on their movements. If they are in a cast animation that you know can deal damage, immediately cast your Q to gain a shield. Ki Barrier is deceptively large of a shield and it will be able to negate majority of poke damage early on in the laning phase. Basically meaning, if your enemy only has one way to damage you from afar, with correct timing, you are invincible in lane. However, if you stay at a range to where the only way an enemy can damage you is poke you then you are missing CS, which is bad.
So, the plan here is to, before your opponent can do anything, be sure to get your spirit blade next to you with a Q. Next, if the opponent is poking still Q and DONT BASIC ATTACK THEM! Minion aggro is extremely important due to Shen's low stats and relying on active mitigation and the constant damage from minion aggro will wither you away quick. Instead, use your Q enhanced hits to instead be used as farm assist. While I told you not to do this, this is fine here since you were using your Q to negate poke and you are in melee range to farm. If your opponent full on engages you, using your W to get Ki Barrier up and the dodge buff will allow you to become the closest thing to immune to damage FOR A TRADE in the game without being an ultimate or invulnerability. Why? Dodging negates basic attacks and the shield is enough to block one spell, meaning the enemy will have to fully unload on you if they plan on doing any damage.
If the enemy is attempting to use their full rotation you, then it is time to engage if you can. You need to give them some damage back with a quick Q and E. This is what trading is. They full rotation, you full rotation. However, since you use Energy and if they use Mana, then you can do this nearly as often as you want. Anyways, that's the basic defensive pattern as Shen.
Moving onto his offensive pattern in lane, he works in ways that you wouldn't see at first. First off, Shen's version of poking in Top Lane is not with his Q, but with his E. Why? Heck, remember what I said about minion aggro? Thats innately letting the enemy get free poke back at you. Instead, deal damage with your E, get Ki Barrier, and then have your own minions aggro onto the enemy for additional damage. Remember to not basic attack them so the same doesn't happen to you. Shen's full rotation offensive, as I call it, is what you would think. Q to get the blade in position, then EQ and W if need be. This will allow Shen to pull off as much damage as possible. If you dont kill them with one EQ, then you likely wont be killing them unless you have an ally with you to crowd control them further.
As a standard rule, once you hit Level 6, look out for good ultimates. Dont ultimate for everything even if they tell you to. If your ally has 3 enemies destroying them, they are gone. Your shield isnt that good until Level 16 really. Anyways, instead of all defensive ultimates, you can also do some offensive ultimates by using your ultimate on invisible allies like Rengar and Twitch to set up some crazy combos, making Shen a true ninja. Securing a kill with a Shen ultimate is always great.
Team Fights
You are out of the laning phase and now the team fights are breaking out. Or maybe this is during the laning phase, but its time to secure a Dragon and your ultimate is up. Either way, this applies. Your standard role in a team fight is to protect allies and damage enemies at the SAME TIME! How? Communication thats how. Who says you need to use Q? E into the enemy team yet leave your Spirit Blade at whoever you teleported to. If the enemy team is smart, after the E, they will focus the squishy and not you IF THE TEAM FIGHT ISNT A MASSACRE TO BEGIN WITH. Anyways, use your W to help mitigate half of the forms of damage that that ally and allies around the Spirit Blade would take, especially these days with people like Jax running everywhere. Of course, if they begin to focus you, Q immediately and W as quickly as possible. If you die before you can Q and W, then you engaged into the wrong fight or bit off more than you can chew. There should be another front liner on your team so you aren't absorbing ALL the damage.
If the enemy team is winning the team fight, a cool trick you can do is E behind them but not hit them with the E and then Q before they react to slow them since they are likely chasing your team and since you just E'd behind them, they will be slowed. While this leaves you vulnerable, Shen can get out of some serious stuff if he plays his cards PERFECTLY. So you dashed and then slowed, now you have escaped.
Sometimes, if you have a sustained damage melee carry or Melee ADC, then you should instead wait for the other front liner to engage while you ultimate the Melee ADC so that they become much tankier during their initial dive. Not to mention you get to join the dive once it's done, giving the Melee ADC a taunt to keep the enemy in place and kill them. Don't do this if your Melee ADC is too ballsy though since then he will just die then.
Thats all I got for you.