Lady Vashj is all about the mana control. Having high mana means you have a bigger shield, more Frost Arrows, and the ability to cast spells, but low mana means you deal more damage (sorta). It's a balance, you want to expend mana to get lower in health to deal more damage, and with each kill you restore a lot of mana which allows you to keep casting spells and will make you slightly stronger in the future. Try and keep your mana around half full when possible but don't waste it pointlessly. All of your damage comes from basic attacks without Heroics, and although you don't attack as quick as other ranged dps you do hit pretty hard with powerful individual basic attacks. She works well against basic attack heavy teams or on teams with good engage.
Frost Arrows provides a ton of utility, making enemies have a very hard time running away from you as you continuously peck at them with basic attacks, and if they try and turn around in frustration you slow their attack speed as well and can start kiting them. It also drains mana, which is bad because it drains mana, but it's good because it drains mana (you follow?). Rain is a nice utility spell that makes it easier to escape and will let you keep your mana levels stay at the level you want them at, while also being a nice buff for your allies as well. Mana Shield is your real defensive ability, blocking a ton of damage and again tying in with the mana conservation act.
Tidal Wave deals decent AoE damage, but the movement speed it grants your allies is great for initiating and can get you places much faster. The mana cost is pretty hefty which will encourage players to use it offensively to possibly get the mana refund, but it can still be used as an escape of course, and as a side note it's pretty much your only form of spell damage. Whirlpool on the other hand, if you can stack up attacks on a target it can outright kill them, but bear in mind that in order to get the benefits of the ability the enemy has to be close enough for you to attack them, so keep that in mind when targeting enemies even if you want to place it on a squishy. Even though the ability slows it isn't a huge threat in itself unlike Purifier Beam, instead it makes you more scary to that enemy, so position yourself accordingly.
During fights you can position much more aggressively than other marksmen due to all your defensive options. You don't have high basic attack speed but you hit like a truck and debuff them heavily, so each basic attack you fire is a big deal and you can't afford to sit back safely. You want to peck at the most damaging or mobile of the group in order to weaken them while letting your allies handle the warriors. When enemies engage of course try and slow the advance of the enemy's initiators but whenever possible chunk their backline with an attack or two. When they run you can slow them for easy pickings and easy kills.
I would go a hybrid damage built with Chilled to the Bone, Drawstring, Healing Rain, Whirlpool, Slippery Eel, Frozen Arrows, Infused Arrows.