This build is designed to provide a strong level 1 gank in bot lane. The core idea of this build is that Shen's 1.5 second taunt at level one can be used for a strong gank. If this gank fails, Shen's kit still allows him to give his carry some sustain through Vorpal Blade.

You should only pick this build with a carry that is prepared to gank at level 1. Good teammates are Vayne, Sivir, and Caitlyn with a bit of luck (draw them into a trap with Shadow Dash). Have your support get Ignite and/or Exhaust to improve the gank.

Playing support instead of jungle or top means that you will get less gold and be less tanky in the late game. Your role in teamfights is not to take all the damage all of the time, but to protect squishy allies by drawing off enemy melees through use of Shadow Dash and healing the entire team with Heal and Locket. Accordingly, you want your jungle and top players to be tanky dps like Lee Sin, Udyr, Gangplank, and Irelia. Fortunately, every top these days plays tanky dps so this should not be a problem!

Marks:
Magic penetration gives a stronger poke with Vorpal Blade.
Seals:
Flat armor provides a strong early game against the opposing carry.
Glyphs:
Magic resist per level is always useful. Flat magic resist would probably be superior against a bot lane with early magic damage, like Sona, Starfall Soraka, or Taric as support or Ezreal, Corki, or Miss Fortune as carry. Flat cooldown reduction could also be useful, but I haven't tried it.
Quintessences:
I pick flat HP because I intend to do a level 1 gank. I think these runes are a bit overrated for most characters, but Shen does benefit a lot from HP, improving his and his carry's sustain from Vorpal Blade. Move speed is another option that would provide more all-around benefit.

Offensive:
Summoner's Wrath improves the damage of your level 1 gank by reducing the exhaust target's defenses. I think it is worth sacrificing the additional point in Enlightenment.

Defensive:
Our defensive masteries improve armor against the opposing carry, increase HP and HP regen so more sustain is given by Vorpal Blade, and increase CDR for our ultimate later on. Siege Commander also improves our ability to do solo lane pushes, a style that is quite strong with Shen's ultimate.

Utility:
I pick utility because it gives us gold to make up for being a support, and because it allows us to start with Ruby Crystal + health potion for greater sustain.

Summoners are picked for the greatest level 1 impact. Shadow Dash into Improved Exhaust will tie up your target for a long time and weaken their defenses. Heal will ensure that your enemies cannot win the level 1 fight. In the midgame, these summoners will allow you to turn around ganks on a solo ally in top or bottom lane with ult -> heal, followed by shadow dash -> exhaust when the ganker tries to run.
What we sacrifice by taking these summoners is the ability to lane push more effectively. Teleport really shines with Shen's ultimate, allowing him to be everywhere at once. If you decide to take Teleport, I would recommend replacing Exhaust and moving the mastery point into more CDR, and moving the filler point in Improved Recall to Summoner's Insight.

Skills are highly dependent on how the lane is going.
If you are with someone who wants to do a level 1 gank, you can get Shadow Dash first and make a strong initiation along with Exhaust. This is what you should aim for, because otherwise a different support would serve them better. If your carry won't go along with you, level Vorpal Blade first to give poke. Use it on minions with full HP in order to give some sustain to your carry.
If your initial gank succeeds, congratulations! You can continue to put pressure on the lane by leveling Feint at levels 3, 4, and 5 with one point in Vorpal Blade at 2. This will allow you to continue to make strong ganks with Shadow Dash -> Feint. If your gank fails, put more points into Vorpal Blade and use it to heal off the damage you took in the initial gank.
In general, you should not use Feint at rank 1 except to shrug off some harass damage. Do not use it in a real fight until it is higher ranked. It is more important to keep up enough energy to keep using Shadow Dash on cooldown. However, it becomes quite good if you max it by 9 and you become a great midgame tank. The tradeoff is that you will be quite passive as it is being leveled up and you have fewer points in Vorpal Blade.
If your carry is farming well and the enemy is zoned out, you can afford to level Feint with one point in Vorpal Blade to poke them back. This gives you a much stronger midgame. If your carry is getting pushed back, level Vorpal Blade instead to give some harass and sustain.
You should not put more than one point into Shadow Dash, because its taunt time and energy cost remain the same.

Ruby Crystal + health potion start is quite strong. After our level 1 gank attempt, we can heal off the damage with the health potion and Vorpal Blade. Hopefully, our enemies will be scared enough that we can use Vorpal to regenerate our carry as well. I would recommend going straight for Heart of Gold to maximize its GP10. Boots are really needed to keep up with enemies, and I would recommend building them up next. Always go for Merc Treads unless your enemies are very heavy in autoattacking AD, in which case build Ninja Tabi -> Randuin's and win the game. Otherwise, follow up with a Aegis to improve your teamfights, as you should now be into the midgame.
Once the midgame begins, your item build becomes more situational. If your team is pushing as a group, go for Locket of the Iron Solari and Zeke's Herald, order depending on how squishy and AD focused your team is. If you are getting focused by the enemy team, you can go for Warmog's right away and punish their stupidity for attacking the tank. You can build into Atma's and get tons of damage off of your health-scaling abilities as well.

Shen excels at saving overextended allies from ganks. With this build, you can ult in, hit Locket for an additional shield and taunt away using Feint. As you begin taking damage, hit Heal to give even more aid to your ally and yourself. You can usually turn around a one- or two-man gank into a kill, even with support items, but you should not try to save an ally from three or more people; you simply don't have enough tankiness with a support build to pull it off.

If your team has a strong pusher like Sivir or Nasus, tell them to push a lane while the rest of your team occupies the enemies at middle. Keep a close eye on your enemies and try not to engage! You will probably lose a 4v5 team fight. Wait for one or two of the enemies to break away and attempt to gank your pusher, then go in once it becomes 4v4 or 4v3. Then, as the gankers reach your pusher, ult in and save him. Even as a support, this build should give you enough power to win a 2v2 fight.