Man I think I just suck at shen. I miss his E in lane, I stack his w with the taunt, I w when they're not auto attacking me.
I lost to a yi as shen. Think about that.
I am pretty low elo but I think Shen is just pretty hard. Top lane is full of lane bullies and hyper carries and Shen is neither, just a plain old tank with global pressure. His new kit also has a lot of skill cap -- using W effectively is tricky.
I had a lot of trouble laning with Shen at first and the big thing I did to improve was to use E and W way less. Q is Shen's trading tool and helps him last-hit as well so just using it all the time and walking up to auto your opponent when possible is fine. Then you have E and W to respond to whatever they do instead of trying to use them proactively. Shen suffers from the same pattern as Renekton in that if you do a full combo -- E through them, Q for the trade, W to protect yourself -- suddenly all your defensive tools are on cooldown for 10 seconds, including your shield since you need to use an ability to activate it. But unlike Renek he can't chunk you to half health in one combo, so a lot of the time it's better just to do the minimum unless you think you can get the kill.
When using E, keep in mind that it's variable-length so Shen will dash only to your cursor if it's closer to him than the max dash length. If you put your cursor on your opponent and hit E, and they are moving away from you, you are guaranteed to miss.
Shen also has terrible waveclear, obviously, so you will probably spend a bunch of time pushed under turret. That is okay because it's pretty hard to dive Shen since he can taunt you under turret. But I recommend doing some last-hitting practice and remembering how last hitting under towers works -- two turret shots plus an auto for a melee minion, one turret shot plus about 1.2 autos for a ranged minion (so a Q auto will suffice), about four turret shots and an auto for cannons, and watch how your minions are dpsing as well.
It's also tough as Shen because, as Zky has noted before, other champs get laning pressure at 6 and you don't. You get global pressure instead, which doesn't help you with your matchup. Everybody else gets presents at level 6 -- Shen gets responsibilities. To win the game you need to use your ult both effectively and constantly. You want to ult into a close fight or heavy trade, turn it into a kill fast, and then be proactive in finding an objective to grab afterwards. Ideally while your opponent is backed so you don't lose your turret right away.
It's bad to ult somebody who won't benefit from the shield but it's worse to ult somebody who dies before you get there. It's also bad to ult in somewhere and then not actually have anything to do. When I'm in top lane I tend to splitpush a bit and use the ult for offensive pressure and TP for map positioning.
Shen has a lot of weaknesses -- his AoE CC is pretty poor, he is not great at pushing turrets or sieging, and he lacks stickiness to secure kills. In exchange he gets a lot of damage for a tank and tons of mobility and global pressure, plus a very powerful teamfight ability with W.