Ezreal has gone through some tough times both as an AP mid and AD carry for years. For now he is at an awkward position being neither the best nor the worst, but surely on the worse side. Of course if played correctly he can be godly, but for most of us average players we wont be hitting every skillshot and sidestepping nukes easily. I am here to guide you through how to not lose as Ezreal, as he pretty much sucks right now.

I am a lowly silver 5 player at NA server from HK. I've played Ezreal since season 3 and has been playing him only. I have used the mystic build back in season 4 and everyone told me it sucked, and right now it becomes the standard build :). I suffered a constant 170 ping right until the migration of the server, which raised the ping to a whopping 212, which forced me to play TW server ever since. So don't worry, it's still possible to succeed as Ezreal under high but stable pings.

Pros:
-High ranged spells
-AS steroid available since level 1
-"OP" escape

Cons: why Ezreal sucks
-Really bad laning phase
-Demanding at teamfights to be successful
-W is pretty much just a refresh for passive

This is when Ezreal is weakest. (Doesn't matter which build path u go)
Don't even think of trading evenly with the enemy.
The enemy is not stupid. They stand behind minions so you can't even hit them with your Q.
Usually the enemy will play confidently and walk up to pressure. Do not fight back. Just walk back and poke with your Q when they overextend.
Before getting tear, conserve mana by only Qing a minion only when necessary. Try to CS with autos only.
Try not to lose the farming game and just wait for midgame.
Remember to stack tear by using spells every 4 seconds.
After you recall, spam Q and W to get 2 free stacks before shopping. W into E then spam Q back to lane. Avoid spamming W when walking to lane to conserve some mana for laning.
Ezreal has low base HP so fights to the death are not advised at all.
Just remember if you don't lose early game, you auto win mid game.
JUST FARM LIKE A *****

Alright so you finally struggled through the laning phase and it is time for some action.
At 25 miniute you are expected to have 2 items, Muramana and Trinity Force.
Activate Muramana after shooting a Q to poke enemies down with surprise damage.
When fights erupt, do not run in blindly and starting attacking the closest target.
Find a safe spot and Ult the enemies first. At mid game Ult as many as you can. When your ultimate starts doing insignificant damage to tanks, switch to Ulting the carries so your assassins and bruisers have an easier time slaying them.
Teamfighting as Ezreal is tough as you cannot stand still and fire everything and expect to win like a Vayne. You have to auto attack the closest threatening target and try picking at enemy carries with Q. Ignore super tanks that don't threaten you as Ezreal is a bad tank killer.
Your job is to stay alive. Do NOT E in to finish off an enemy if you are unsure if it is safe. Keep it for repositioning.
Keep auto attacking to proc muramana and use Q and W whenever they come off cooldown between auto attacks. Do NOT cancel an auto attack just to cast a spell unless it is E or flash.
AUTOS>SPELLS if you are unable to keep track of ability timers.

Remember to turn off muramana before and after fights to conserve as much mana as possible because the active scales off CURRENT mana. So having more CURRENT mana means more DAMAGE.

Ezreal is fun, but it takes a lot of commitment to play him well.
Honestly I would ask what you are doing with your life if you pick Ezreal.
But if you finally do, I hope this helps you succeed in playing this lackluster AD carry, who is unfortunately my main.