General DiscussionHow can I improve with Phoenix?

Don't go mek you don't really have the mana pool to support it.
Maxing birds is the way to go, they have a lot more effect early on.
Don't go Aghanims, it's not very good.
You can get an urn if you really must.
If you can predict an aids lane then buy a tp, ward the camp and dive into the trees as early as possible and stay there till the creeps are back at your tower then TP to it.
If you can't solo kill your lane at six, then TP to another lane and get a kill there. Don't be idle.
Midas is a viable option cause the higher your level, the harder your bird is to bring down in egg. e.g 6-11-16 (the faster you get there the better.
Use birds when the carry is coming into last hit the creeps, you will get him 99% of the time and it will fuck up 1-2 creeps for him.
Dive over creeps and drop birds when your dive is on top of them and ult.
Birds don't stack.
If you go shivas' use it before you dive not after, this has a much larger area of effect if you do.

I might be missing somethings.....dunno.

Be patient. Understand whether enemy has the tools to take down you or your egg before they die. Hit your birds one at a time unless you're using it during icarus dive to dish out some damage. Always check to see how much mana you have and do a mental calculation whether you can use your skills.

In my opinion, the most important thing about Phoenix is knowing what heroes can mess you up in laning phase and you have to keep an eye on the map all the time.

what havoc said, although i personally don't like midas as it is over half of a veil/atos which are just so damn good
let range creep go first if you think you will be in a hard lane
4-4-0 is good when you are doing decent or want to snowball
1-4-4 if you are unbelievably behind/your other cores are really strong/deathballing and need heal/have heroes like lc on team
mek sucks because of mana problems. the items i get are from: tranqs urn veil atos shiva refresher, situationally bkb eul book vlads
learn to position egg well. think what you want to achieve - zone the other team? draw aggro so your allies can crush them? not die?
at late game, sun ray is stronger than egg in quite a few situations so don't be too hasty to egg
all of your skills except egg are usable at the same time, learn to abuse this
e.g. throw spirits while you are using sun-ray, and toggling movement on and off to get the best positioning. atos works wonders for this as it has similar range to all his skills
you can tp during dive/sunray
you can move in sunray even when entangled/ensnared

Sunray against heroes that have ensares, (Axe, LD, Naga) you will get out 100% of the time.
Don't be afraid of man modeing for your team. You are the iniatinor, let your team know when you'll go in, and hope their follow up his good.

Try not to waste all of your mana in lane, (Unless you are a mango fiend.)
You don't really need gold, all you need is levels. Focus on staying alive and getting levels.
Egg is FRAGILE. Find a good time to use it, and in the later stages, find a good spot to use it.
Don't be afraid to be defensive with your spells. Dive is actually a good slow, and you can use it to save a teammate who's being chased by someone.