Unlike some more popular healers, Alexstrasza lacks Crowd Control, like Entangling Roots for instance. She also does not have a Cleanse in any form. On the other hand, Alex brings a lot of healing, including percentage based healing, which can be very good for high HP heroes like Diablo for instance.

Alextrasza has a baseline mana refund mechanic on her Flame Buffet ability for hitting targets that are already burning from it, which grants her very good waveclear in PvE. Always spam this ability on minion waves, but be careful against heroes, because if you miss too much, you are going to run out of mana very fast.

Alexstrasza also has Dragonqueen, which is basically a second ultimate ability, and that in itself is a reason to pick her on some maps like Infernal Shrines. If you are playing against Alexstrasza and you see her turn into a dragon, you should generally disengage from the fight, unless you already got a strong advantage with a few kills for instance.

There basically are 3 build paths for the Dragonqueen, one based on Gift of Life, another on Abundance, and the last one on Flame Buffet.

The Flame Buffet build is very fun and quite popular, unfortunately it is not reliable and only becomes powerful when reaching Level 20 with the Ancient Flame upgrade, and you will often lose before that point due to having a very subpar build.

The other two builds will be explained bellow.

This is the build I generally recommend in Storm League.

At Level 1, Live and Let Live will reduce the cooldown of Gift of Life as long as Alexstrasza is healthy enough.

At Level 4, Exuberance grants Alextrasza 15% Movement Speed while she is healthy, making her much harder to reach for her enemies, and enabling her to maneuver around fights more efficiently.

At Level 7, Lifeblossom completes the Flowers Build, making it so Gift of Life no longer costs Health as long as Alexstrasza is healthy, and continues to collect the Flowers dropped near the heroes she heals.
Note: The talent reduces the base cost of Gift of Life from 15% to 10% of Alexstrasza maximum HP, but the amount healed remains based on the original 15%, there is no hidden downside!

→ With this in mind, the build is played like this: You heal allies with Gift of Life and collect the Flowers with the movement speed you have. In case you still take damage and are no longer healthy enough for the build to work, it is time to use Abundance to heal yourself, even if your allies don't join in the circle! If this is not enough and you cannot retreat, it might be time to use Dragonqueen to turn things around.

At Level 10, Life-Binder is another tool to make yourself healthy again when in trouble, but it of course is also a great ultimate to save an ally in case they are being focused instead of you!
Cleansing Flame is also a great choice as you can no longer be focused while flying. This ultimate also provides healing to your entire team instead of a single target; while Life-Binder makes more sense with the Flowers Build, Cleansing Flame can still be picked if the enemy team is more AoE oriented than single-target.

At Level 13, I generally recommend Pacify if there is any problematic target in your range. Divers like Illidan or Genji become way less scary when you make them tiny, but using it on a Jaina who just got a Ring of Frost might prevent her from killing your whole team as well!
Life Unbound is also a good talent in case the enemy if focusing one target, it can really help saving an ally to guarantee Life-Binder goes off! However, note that any Healing Reduction on the enemy team will make you want to pick Pacify more.
The third option, Dragon Scales, can be picked if the enemy team if mostly focusing you with CC, 50 Armor will let you survive most of those situations.

At Level 16, I overall recommend Draconic Discipline. You're entering the late stage of the game, where winning a teamfight can mean winning the game, and that extra duration on Dragonqueen is often more game winning than the other options.
Tough Love grants your teammates even more sustainability with the 30 Armor it provides, so it is a fine option as well if your game plan is to keep that one target alive at all costs, it is a good pick with Cho Gall for instance, but otherwise you probably picked Alexstrasza because Dragonqueen is good on the map, so empowering this part makes more sense.

At Level 20, the Blessing of the Red is my default choice, it simply makes your allies much harder to kill.
If the enemy team has a lot of Percentage Damage based heroes like Tychus, you will not want it.
If you get to Level 20 and need to take a decisive fight instantly, you will not want it either.
In both of those cases, Ritual of Life is the pick, and it is also the pick if you are trying to keep this one target alive at all costs, it is again awesome with Cho'Gall.

The Globes Build is more dependent on your team, as you will need your allies to gather in the circle of Abundance to get proper value out of it. It requires very good awareness of where to place the circle, so your allies can get healed without making them an easy target for enemy abilities! Teammates can either fail to join the circle, or get in so early that they stand in place and become easy prey; for this reason, I do not recommend this build until higher ranks.

Nonetheless, At Level 1, Circle of Life is a quest that will increase the healing of Abundance and eventually spawn a Regeneration Globe as well!
A popular and strong combo with this is Mephisto with Spite at Level 4, in which case your goal is to gather 15 Globes ASAP in order to gain the ability to spawn globes yourself. When this is achieved, Mephisto is almost always boosted by the globes, and it will be a nightmare for the enemy team, as the hero can win fights almost by himself.
→ If you find yourself playing with a Mephisto, you should pick Circle of Life even if you pick other talents after.
→ If you find yourself playing against the Alexstrasza + Mephisto combo and they are good, you do not want to fight them! You need to avoid fights and slowly apply map pressure until they cannot handle it, no matter how counter-intuitive it seems, that is the correct way to counter the Alex + Meph combo.

At Level 4, Surge of Vitality is the default pick, but if you need to move around more yourself than your allies Exuberance is fine, and if you really like the slow from Heat Exhaustion AND you are good at landing it, it is also a good option.

At Level 7, Verdant Flourish is the pick that makes most sense, but if you find yourself placing Abundance in the fray while staying back, it might be better to pick Fire Within, again only if you are good at hitting it consistently!

At Level 10, Cleansing Flame is the default pick for the build. Generally in teamfights, you will want to use Abundance, then use Dragonqueen, then use the empowered version of Abundance. You will normally not have time to use a second empowered circle before your trait ends, however Cleansing Flame will pause the duration of Dragonqueen when you use it, which, when you land, will enable you to use Abundance one again before the end of your trait!
This is an all-or-nothing tactic, where the enemy team basically cannot contest the area while you're using both your trait and your ultimate.
Nonetheless, it is possible to pick Life-Binder if you're supporting one specific hero, to make him unkillable, and once again Mephisto generally will want that so he can wreck havoc freely!

At Level 13, Life Unbound and Pacify are once more contesting each other. You generally pick this build for high HP targets, so Life Unbound makes more sense, but if you think Pacify can really shut down that one problematic hero and win fights, go for it!

Level 16 and Level 20 are the same as before with Draconic Discipline and Blessing of the Red as default.