Something incredibly important to note; ALWAYS safeguard into a gank if you can. Safeguard is the safest (totally intended) way to get into a gank, and give you positioning to apply cc (red buff/cripple)
Many people dont seem to realize that leading with safeguard lets you get your full combo off (tempst, autoattacks, cripple, autoattacks, sonic wave, autoattacks, resonating strike, autoattacks,) instead of cutting off a lot (if you initiate with sonic wave/resonating strike, you lose some autoattacks, and lose earlier cc. Its also so easily dodgeable)
Try to avoid casting resonating strike early, as well - Land the sonic wave, then wait as much as possible to bait their flash/blink/etc, unless you know its down/they already used it. Remember that if you miss your q, youre pretty much screwed..
I often, if I cant land a good safeguard, will flash into tempest. flashing into tempest saves me the q until, again, they flash/blink, so I can better secure the kill.
additionally, and this should be painfully obvious, dont ult people away from your team. Just dont. If you dont think ult will kill them, and its positioned the wrong way, just dont use it. leesin,even without ult, will deal a lot of damage and be fine. Worst case, just kinda ult someone randomly (like a tank, or someone with cc, shortrange abilities) just to disrupt thing.
During teamfights, youll want to stay out of it until you can safeguard into the fight. If you can safeguard into xin/jax/kassadin/akali etc, they get defense boost through the shield, and you land where you need to be to land cripple/ult.
Remember the rhythm of flurry, and keep track of the autoattack timings in your head if you cant really see whats going on. During a teamfight leesin really needs his energy, so he really needs to autoattack.
Leesin isnt that difficult to use, but hes very difficult to master. A good leesin will take command of a game from start to finish, carrying sometimes almost unnoticably. He can easily set up kills for a carry to pick up, particularly during laning. Lategame his abilities are just incredibly good because of their awesome scaling, and just general utility (60% slow/ attackspeeddebuff, two blinks, aoe knockup ult)
tl, dr - Safeguard into things. Cripple is your friend. Dont miss qs. Carry hard.