Energy Management and Abilities
The first thing you'll notice when playing Shen is that instead of a mana pool, the resource you will be using is Energy. It is a static pool of 200, and recharges at 10 energy per second. All of your abilities (with the exception of your ultimate) cost an amount of energy, depending on the level of the ability (reduced over subsequent levels). Since energy is very limited, you must know exactly when to cast each abilitiy and how to effectively use it to conserve your energy and use the right combination at an opportune time.
Passive: Ki Strike
Every 8 seconds, Shen's next auto attack will deal magic bonus damage. Every time he is hit, the cooldown is reduced by 2 seconds. The bonus damage scales with his health (10+ 5 x level + 8% bonus max health).
Abuse this passive every time it is up! Poke enemy champions or last hit more easily. This passive allows Shen to jungle as he will be able to deal more damage to jungle creeps. The damage it can deal is deceptively high. Build HP to use this passive to the fullest.
Vorpal Blade (Q)
Shen throws a sword at a single target, dealing magic damage (scales with .75 per AP). That unit becomes life tapped for 5 seconds, healing anyone who attacks it over 3 seconds.
This is Shen's main damage, farming, and harassing ability. This is the ability that allows him to stay in lane longer, regenerating HP, and also to jungle. It has a low cooldown, and can deal decent damage to last hit or in-combination with Ki-strike, your passive, to harass enemy champions are in range. If you or a teamate is low on health, use it on a canon minion to heal off of damage delt. This can also be used to sustain your team when doing Dragon or Baron.
Shen shields himself for the next 50-250 (+0.75AP) damage and lasts for 2.5 seconds or until the shield is broken.
This shield can be used to save your life or make you a bit more tanky when taunting enemies or initiating a fight. At max rank, it has a relatively low cooldown and can be spammed as you run/dash away from an enemy opponent. Use it to shield from pokes and other damage when taunting.
Shadow Dash (E)
Shen rapidly dashes to a target location, taunting enemies he collides with for 0.8-2 seconds. If an enemy is struck, 50 energy is returned.
Like Rammus's single-target taunt, Shen's is much better as it can taunt multiple enemies in a small line. This dash can also be used to go through thin walls when chasing/escaping an enemy. If you use this to get away, watch your energy as it can get low and you may not be able to use another skill like your shield (W).
Stand United (R, Ultimate)
Shields a visible allied teamate anywhere on the map for 200/475/750 damage (+1.5 AP) for 7.5 seconds and teleports you to their side after channeling for 2.5 seconds.
Shen's ultimate has a very long cooldown (180, 150, and 120 seconds) and the shield may not be able to save your ally, so effectively knowing when to cast your ultimate separates the experienced from the novice Shen players. Since the spell takes 2.5 seconds to channel the teleport, it should be used in anticipation when an ally is engaged with the enemy. Too early and you may chase off the enemy or used too late and it could cost your ally's life. When used that the right time, you can turn a 1v1 situation into a 2v1 and score the kill.
In limited instances, you can also teleport away if you are trapped, but be wary that ulting a teamate since his ultimate got nerfed, will no longer grant Shen the same shield, so you may still die if you have really low HP.
Leveling Q first allows you to do the most damage and to sustain in lane. Leveling your taunt (E), followed lastly by your shield W is the best way to skill Shen. Of course you should be taking your ultimate (R) at levels 6, 11, and 16.