Hey! Hi, a Shen main here. What seems to be the problem?
A fairly large error I see many Shen players do is using their Shadow Dash to only hit one player, usually the carry. While a good plan, a great Shen will try to line up as many enemies as possible, both for maximum energy restoration and maximum crowd control. Another little error is that many players use it to engage. This is a fairly poor choice most of the time, if you have a better engager like Malphite or Amumu. If you catch them off guard and out of position, feel free to taunt and burst!
A place where teamfights usually erupt is the River, both at Baron and at Dragon. The little brush right next to the curve of the banks is an excellent place to lurk and engage. Most people do not expect a tanky Shen to dash out of there and hit them all, so there's a pretty good surprise there. Always try to surprise them with your taunt, there's plenty of thin walls that you can dash through and get them, provided they're hugging the walls.
I recall a game where I was at enemy wraiths and I saw their Ashe coming from mid to farm. This was middle to late game, already got my Warmogs and my Randuins, so I was fairly tanky. I had warded the little four-way path previously and so I had vision on her. I dashed through the thin wall facing the River and got Ashe completely by surprise. She tried to run, blowing Flash and trying to kite me with Frost Shot, forgetting about Randuins! Such an easy clean up once our Jarvan teleported in.
Just some basic tips:
-Try to land a vorpal blade on their carry or mage at the beginning of a fight. If you're sufficiently geared, the massive regeneration boost can possibly save some of your teammates!
-Always try to help your team take Baron or Dragon, for the same reason as above!
-If you're not doing too well early game or in lane or wherever, skip a level of Shadow Dash and level up Feint. The shield is deceptively strong early game, soaking upwards of 100 damage with a hit of a button.
If you have more questions, feel free to add me in game! I'm not pro, not by a long shot, but I've been playing Shen almost ever since he was released. Happy Taunting!