Ana is a long range healer with great utility, her Sleep Dart providing a good setup for her teammates as well as an interrupt to key enemy abilities and at times a way to shutdown enemy engages, her Biotic Grenade increasing her healing output or denying enemy healing. Her Healing Dart of course providing healing, can also be used to reveal areas, and as such check Bushes! Later on, it can also cleanse Stuns or Roots and Slows. Finally, Nano Boost will make any spell damage based hero a teamfight winner!

Despite all those things, Ana has major weaknesses that make her struggle in the current meta.
First, Ana's healing output is not the most reliable, as Healing Dart is a skillshot, and if you miss too often your team will suffer from it. Then, even if you land your heals, the output is still not impressive.
Second, Ana lacks self-healing despite her Shrike trait; Ana's main self-healing ability is thus Biotic Grenade, and it's not much.
Third, Ana is very vulnerable when getting dived, more than a bunch of other healers; her main tool to deal with those situations is to land a Sleep Dart and pray for teammates to help her. Due to her vulnerable nature, Ana cannot really step-up to get self-healing from Shrike, as she puts herself in a dangerous position when doing so.

Nonetheless, Ana is a fantastic hero and is, in my opinion, extremely fun to play, and landing all those skillshots feels very rewarding!

In most cases, Ana wants to stay as far as possible from the enemy, while providing support from range.
For this reason, the Grenade Build is generally the safest to pick. The great thing about this build is that all three grenade talents are great by themselves, but also synergize with each other perfectly!

At Level 1, Contact Healing will increase the healing of Biotic Grenade by 30% for every hero hit, which means even if you use it on a single target, it will heal for 30% more already! It also increases the damage dealt to enemies, but that is secondary, the key part is that you get extra burst healing to save teammates, or extra self-healing, especially when you have heroes close to you (enemies diving you, allies helping you, or just your long range DPS sticking with you).

At Level 4, Biotic Enhancements reduces the cooldown of Biotic Grenade making it available more often. Additionally, the bonus healing you give to your allies will have increased duration, greatly increasing your overall healing output.

At Level 7, Anti-Healer helps confirming kills more consistently by increasing the duration of the healing reduction on enemies. But this talent also increases the Area of Biotic Grenade by 25%, which has huge synergy with Contact Healing at Level 1!

At Level 10, Nano Boost is just a huge card to play in teamfights. You generally want to use it on a mage like Jaina or Li-Ming, but heroes like Sonya or Malthael will greatly benefit from it, and the cooldown reduction it gives can also be useful for Tanks like Diablo who suddenly have a thousand more stuns available.

At Level 13, Smelling Salts is generally the pick to cleanse Stuns, but Purifying Darts can be picked if the enemy is relying on Roots much more, or if they lack Stuns in general.

At Level 16, Active Reload is the talent that will let you save a target with great burst healing. Sharpshooter can be picked if you are confident in consistently hitting your Healing Dart, but in case the enemy team is trying to burst a hero down, Active Reload should be picked regardless.

At Level 20, Nano Infusion turns your Nano Boost target from a monster to a self-healing monster! It allows them to step up and take on the enemy team with much more confidence. In case Ana dies, it also makes it so your target doesn't need to rely on you to sustain while dealing damage, so if the enemy takes you down but they all die in return, that's a win.
Armored Stance is an alternative pick to try and survive if you get dived on, but generally Nano Infusion will win those late game teamfights more.

This build does not try to mitigate Ana's vulnerability but instead tries to be proactive and even aggressive.
The plan is to sleep targets as a setup, and kill them before they have time to even get on Ana.

At Level 1, Slumber Shells is often picked up to reduce the cooldown of Sleep Dart, it also slows enemies when they wake up, so you will get value out of your sleeps even if your allies wake enemies up instantly!

At Level 4, Overdose is picked to make Sleep Dart pierce all enemies, so you can potentially get a 5-man sleep. It additionally applies 4 Doses on them for a bit of damage and self-heal.
In case a problematic target is diving Ana, Debilitating Dart can be picked to reduce their damage, although it means sacrificing the full sleep pierce. Debilitating Dart can also be used offensively to slow a target by 50%.

At Level 7, Night Terrors will actually let Ana move faster in case she sleeps enemies, letting her reposition to safety more easily; however, it is also an offensive talent that will deal 8% of the target's Maximum Health upon waking up. Add to this a full Jaina combo plus a Biotic Grenade to prevent any heals, and anyone should be dead.

At Level 10, Nano Boost is picked up to win teamfights, especially considering the plan to setup kills with Sleep Dart, you cannot pass up on this damage increase that will guarantee kills.

Level 13, 16, and 20 remain the same as in Grenade Build, for the same reasons.

This build is playable in case you feel like you can step up a little bit. It is also my default build for Storm League.

At Level 1, Slumber Shells is often picked up to reduce the cooldown of Sleep Dart, it also slows enemies when they wake up, so you will get value out of your sleeps even if your allies wake enemies up instantly!
Personally, I still like Contact Healing even in this build, as the talent provides extra burst healing that might be lacking otherwise, as well as self-healing.
Vampiric Rounds should not be picked, you do not want to step up constantly and greed for stacks, it will get you killed against competent teams.

At Level 4, we are picking up Overdose to apply Doses when we sleep enemies, and additionally it pierces all enemies, so you can potentially get a 5-man sleep.

At Level 7, Mind-Numbing Agent will reduce the spell power of enemies for every Dose on them, so up to 50%. This means reducing spell damage, and ability healing!

At Level 10, Nano Boost is still the pick to win teamfights.

At Level 13, Smelling Salts and Purifying Darts are the picks depending on which one you need.

At Level 16, Concentrated Doses will seriously increase your healing output for each Dose applied on enemy heroes. Let's say you hit 3 people with Overdose, this means 12 Doses active, which means 144% increased healing!

At Level 20, Dynamic Optics will increase your attack range and attack speed, meaning you can apply Doses on heroes more consistently to reduce their spell power and empower your own healing output.
At this point, Vampiric Rounds would become reliable and good, but it basically means having no Level 1 Talent until you reach Level 20, and that is not acceptable.

Warning: Managing to refresh your Doses on enemies while also healing your team with darts requires a lot of input, so I do not recommend it for most people. The other builds are easier.