Shen rework's been a blast on the PBE so far. Been watching some Shen play, been playing a lot of Shen. After a lot of both, here's the stuff that I've concluded.
WTF is this new sword thing?
Oh, that's his "Spirit Blade". Shen's Q and W revolve around this thing, so in a sense it's like Orianna's Ball. You will consistently be fighting for position to maximize your lane presence; if you hit the enemy with your Q (which pulls the blade to you, damaging enemy champs along the way), you gain a massive trade advantage as the bonus on your next 3 autoattacks is amplified and you can proc your passive off of it. This extra damage is enough to rip your opponent's health bar in two when played correctly.
Shen outside top lane
Shen is a significantly better jungler after the rework. Twilight Assault's autoattack buffs shred through jungle creeps, while Spirit's Refuge blocks attacks from large monsters, allowing you to use it once your passive shield goes out to maximize your health around the jungle. Although Shen won't exactly be the greatest counterjungler, counterjungling him is a very risky fight due to Shen's ridiculous level 3 when he has access to all of his abilities. Anyone who tries to take Shen on in his own jungle will simply get destroyed unless they catch him with low health for some reason. Of course, Shen's main attractive feature as a jungler is his level 6, applying global pressure with his ultimate which can quickly turn an enemy assassin's all-in sour. Cinderhulk as a jungle item naturally caters to Shen's preference of mid to late game splitpushing with the added bonus of duelling power through Skirmisher's Saber.
Can Shen still do an AP build?
I'm afraid not viably. Shen lost an AP ratio (his taunt now deals HP-scaling physical damage) which puts a big damper on the burst he had before. In addition, Shen can't really take advantage of the passives of Rylai's or Liandry's like he could before the rework. However if you still want to try it for those massive Stand United shields, I would suggest investing in a Nashor's Tooth to take greatest advantage of Shen's Q, but beware its high Energy cost.
Strategy in teamfights
Shen's kit provides the flexibility to perform well in a teamfight regardless of his choice of focus. You can lay back and assist the ADC in fending off that pesky bruiser by shredding their health and nullifying their autos, or you can go deep and just tank the enemy carry, effectively phasing them out of the fight for two seconds. In the time leading up to a teamfight however, the strategy remains the same. Splitpush, solo the Dragon, assist with the Rift Herald, you're Shen, you can do whatever the fuck you want up until the big teamfight.
When you head in though, make your choice wisely as to who you nab with your ultimate. If you suspect a valuable member of your team is out of position and is about to get caught, the shield from Stand United can be a one-way ticket straight into the middle of the enemy team. That is definitely what you want to do. Hell, you can just ult your charging-in front line if you're far enough ahead. Taunt in and pop Spirit's Refuge to completely nullify two or three members of the enemy team for just long enough for your team to make the move. If all goes well, you've bought enough time not only for your teammate to escape, but for the team as a whole to act on the advantage you've asserted and thoroughly rout the enemy.
One last thing to remember
Spirit's refuge causes you AND your allies to block attacks from the time it's up.
More to be possibly added to this later on!