Shen is an interesting guy, his Stand United can turn a 1 v 1 into a 2 v 1, or give someone a massive shield during a teamfight. His Spirit's Refuge can also save a carry from dying. Shadow Dash can also CC enemies for your teammates to follow up on easily. While usually seen Top more often than Support (I've also seen Shen Jungle), Shen can be very useful in a team, especially in teamfight-oriented comps based on protecting a single carry.

Flash - Always taken on almost every champion, including Shen. Not only can it extend the range of his Shadow Dash, he can use it to escape abilities and quickly reposition himself.

Exhaust - This is great for a support. Not only can it save you or your teammate's life, it will make any huge threat much more manageable. Especially good against assassins such as Zed and Akali.

Ignite - While the usage of it falls off later on in the game, early on it is great for securing kills on low health enemies and applying Grievous Wounds to champions such as Vladimir.

PRIMARY TREE

Aftershock - One of the only two options in Resolve, the other being Guardian. Going Grasp of the Undying isn't optimal since when you get in range for an AA you'll be poked out by the enemy ADC or Support since they'll probably outrange you. Your Shadow Dash will proc Aftershock and the raw resistances you get from it will keep you alive.

First Row

Demolish - With turret plating giving so much gold, this will be a great option early and later on in the game. Early on you can chunk down turrets for +160 Gold, while late game when you're much tankier pushing turrets will be even easier.

Font of Life - If you feel like you can't pressure lane enough to get Demolish off, Font of Life is still a good option to provide a little more healing for your team when you engage with Shadow Dash.

Second Row

Bone Plating - This is a great option for Shen as a support since it'll take off some damage from when he goes in for a taunt. Can also be switched with Demolish if you feel like you can pressure the lane to their turret often enough to bring it up.

Conditioning - Both Conditioning and Second Wind are great runes, however I prefer Conditioning since the extra resistances are very helpful lategame. Second Wind should be taken into a poke heavy lane, such as Caitlyn.

Third Row

Overgrowth - More HP = More tank. Again, this is a personal preference and Revitalize is also a good option. The extra shielding on your Stand United can save someone and from Ki Barrier to take more damage. Unflinching is kinda "meh" since his only engage is Shadow Dash and that will put him in the front already.

SECONDARY TREE

Zombie Ward - As a support your main job is to control Vision. Adding more wards will help your team even more when you use Oracle Lens to clear out enemy vision.

Ultimate Hunter - Getting Bounty Stacks shouldn't be a problem as when you use Stand United on someone, you'll get an assist for shielding them. This will basically function as The Ultimate Hat.

Knight's Vow - Very useful for protecting your ADC and making yourself tankier, as well as the 10% CDR.

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Locket of the Iron Solari - Similar to Redemption it can save everything with the massive shields you'll be giving everyone. Take Locket if the enemy team has a lot of burst, such as against a Zed or Syndra.

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Oracle Lens / Elixir of Iron - Oracle is essential to Supports so they can clear out wards and disrupt enemy vision for that sweet, sweet vision score. Elixir of Iron should be bought when you can't buy anything else before a teamfight is going to happen, or when it hits late game and you need everything you can get.

Redemption - Every game picking one up is very important because you can turn a losing teamfight around with a massive heal and burn. Take Redemption if there are a lot of dragged out teamfights or skirmishes.

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Shurelya's Battlesong - Talisman brought back. Using this to engage with your Shadow Dash or another teammate's ability is great, or you can quickly run away with your team to reposition.

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Zz'Rot Portal - Splitpush power. Not really much else to say about it.

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Mikael's Blessing - Use this to prevent CC on someone such as your AD Carry if the enemy team has champs such as Leona and Maokai.

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Frozen Mallet - The 700+ Health from this will make Shen even beefier, and the slow from auto-attacking can help your team follow up more easily. Since Shen engages with his Shadow Dash + Twilight Assault Combo he can easily apply this onto enemies.

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Engaging Fights

You will always be using Shadow Dash to taunt enemies, preferably the ADC and/or anyone else reliant on basic attacking.
Looking for angles and opportunities to taunt both the enemy ADC and Support along with your good early damage by using empowered Twilight Assaults can secure lane pressure + kills.

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While it might not seem like much, an empowered Twilight Assault doing 4% max health damage is extremely good for chunking down HP early.
You can continue to use Twilight Assault in lane just to reposition it, like in either bottom brush or the top part of the lane to ensure it passes through enemies.

By hitting an enemy champion with Twilight Assault you also slow them when they move away from you.

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Spirit's Refuge is another great ability for going against ADCs botlane, after your shielding from Ki Barrier wears off you can press W to completely negate basic attacks. In some cases, you might not want to use Twilight Assault when engaging with Shadow Dash just to be able to use Spirit's Refuge on your ADC when they get focused in a fight.

Apart from just pressing R on someone across the map to TP to them, you can still use this in the middle of fights because of how powerful and long the shield lasts. Always keep an eye on your teammate's healthbars to see whenever someone drops to a low amount to maximize the shielding.