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Li Li, from the Warcraft universe, is a ranged support that excels at keeping her teammates alive during the heat of battle. Her strong healing is balanced by a relative lack of damage and she has less crowd control than supports such as Uther or Malfurion.
What makes Li Li such a good choice for new players is the fact that three of her skills are smart targeted, meaning that the ability will choose its own target. Healing Brew (Q) will heal the nearest ally for a decent amount of health. This ability can heal minions, but will prioritize heroes, so don't worry about friendly minions stealing your heals. The obvious downside to this mechanic is that you can't prioritize which of your allies you want to heal - apart from positioning yourself such that the ally you want to heal is closest to you.
Cloud Serpent (W) is a targeted ability that summons a serpent to help allies in combat. It doesn't do very much damage, but it does enough that it can help out in team fights or be useful for augmenting Li Li's damage, which is not all that great.
The second of Li Li smart-target abilities is Blinding Wind (E), which does a small amount of damage and blinds the two closest enemies, once again prioritizing heroes, making them miss their next two basic attacks. This is one of Li Li's strongest skills in team fights as it can really help to limit the amount of damage the other team can throw out. It's especially useful against heroes like Sergeant Hammer who rely heavily on auto-attack damage.
When it comes to heroics, I highly recommend going with Jug of a Thousand Cups as opposed to Water Dragon. Jug functions as an amped up version of Healing Brew; it will heal nearby allies for a substantial amount and is capable of keeping entire teams alive.
To be clear, Water Dragon is not a bad skill to choose, as it is on a very short cooldown and provides Li Li with some much needed damage and one of the strongest slows in the game. I simply do not think it fits her role as a healer nearly as well as Jug of a Thousand Cups.
Fast Feet, Li Li's trait, grants a movement speed increase whenever she takes damage. This makes Li Li one of the hardest heroes to chase in the game as she can keep herself alive and stay out of the enemy's range.
As for talents, at level 1 I recommend picking up Conjurer's Pursuit for the mana regeneration buff, otherwise you could find yourself low on mana during extended team fights. However if you're confident in your ability to manage your mana, then Pro Toss can be a strong option for the increased range of Healing Brew.
At level 4 I'd advise going with either Healing Totem or Mending Serpent. Healing Totem is a great way to compliment your already strong healing by placing down a ward that heals all allies in a large area. If you plan to use your Cloud Serpent a lot then Mending Serpent, which adds a healing component to the skill, can be fairly strong, but overall I prefer Healing Totem simply because it can heal your entire team.
The Good Stuff is gained at level 7 and adds a healing over time effect to Healing Brew. In my opinion, this is one of the most important talents to pick up if you are planning on going for a pure healer build on Li Li. However, if you are having mana problems, then Pitch Perfect will reduce the cost of mana on your Healing Brew, but if you've taken Conjurer's Pursuit you shouldn't be running out of mana enough to need the help from Pitch Perfect.
At level 13 you once again face a difficult choice, as both Shrink Ray and Hindering Winds are strong talents. Shrink Ray, which reduces the target's damage and movement speed by half, is one of the strongest support talents in the game and is great for helping to focus down a single target early in fights or for securing kills on fleeing targets. Hindering Winds applies a fairly strong slow to your Blinding Winds skill. It isn't as strong as Shrink Ray, but it is on a much shorter cooldown and can hit two targets at once. The choice is really a matter of preference, but I do recommend taking one of these talents, as Li Li is sorely lacking in crowd control.
If the enemy has a lot of crowd control on their team, then Herbal Cleanse at level 16 can be lifesaver, since it will allow your Healing Brew to remove all CC effects on the target as well as grant a movement speed boost for a short time. If the enemy team is not heavily reliant on CC, then Two For One is the best choice in this tier as it allows Healing Brew to heal two allies for the price of one - albeit with a slightly longer cooldown.
Storm Shield and Bolt are always strong options at level 20, and the upgrade to Jug of Thousand Cups can be very useful as it allows it to heal two targets at once, but I prefer Kung-Fu Hustle, which makes your cooldowns recharge at a much faster rate while Fast Feet is active. This is is great in teamfights and can allow you to get off multiple ultimates in a single fight.