Welcome, Ezreal is one of my favourite characters and I like to play him hybrid because it gives me nice burst damage with some sustaine damage aswell a high mobility in the battle.

Pros :
+High Mobility due to 40% CDR
+Nice burst damage aswell good autoattacks
+Global Ultimate
+Can fit as an AP Carry, AD Carry or Hybrid Carry
+Versatile Mystic Shot that can apply on-hit effects
+Epic Dance !
Cons :
-Squishy
-Easily countered with a stun/silence or anything that prevents Blinking
-Skillshot Based

I take Armor Penetration and Magic Penetration runes to improve my early game and allows me to deal better damage against tanks.
Armor and health runes are here to make me less squishy but if you prefer, you can switch Armor runes for Magic Resistance runes to make you more durable against Burst damage

My Masteries are pretty simple, taking the Armor Penetration and Magic Penetration because we all know that hybrids lack penetration against armor and magic resistance.
The last tier of the offense mastery is good because it improves our ultimate damage if we use it to finish runners and improves our chances of getting a kill.

My items are mostly hybrid items. Nashor's Tooth + Ionan Boots of Lucidity gives me 40% CDR allowing me to always have my blink up when needed.
Mystic Shot can procs both the Slow of Phage and the Damage of Brillance. The damage is very nice early and add a lot to my burst while the slow allows me to become a god of kiting !
Gunblade is just a must-have for hybrids. The damage makes your attacks better and the double vamp give you a lot of sustain.
Guinsoo Rageblade synergise well with your attacks and gives a very fast attack speed. Also, your Mystic Shot gives you 2 stacks of Guinsoo if you hit the target.
Archangel Staff gives some Ability Power but the must important is that it gives limitless (almost) mana so it's very rare you get Oom late game.
If the enemy team have some hard CCs and burst damage (Kassadin is ezreal's worst opponent) you should exchance the CDR boots for Mercury's Treads.
Some other good items :
The Brutalizer : This item gives some CDR, good damage aswell a nice armor penetration, very useful at early game as it makes your attacks pack a punch.
Manamune : If you want more AD, you can exchange your Archangel's Staff for a Manamune
Malady : Good early-medium item, it gives you a magic resistance shredding Mystic Shot aswell adds some magic damage to your arsenal
Malady : Good early-medium item, it gives you a magic resistance shredding Mystic Shot aswell adds some magic damage to your arsenal
Force of Nature or Glacial Shroud : It depends on the enemy teamm, get Force of Nature is there is a lot of burst damage and Glacial Shroud if a lot of autoattackers.
I think that evens if Force of Nature doesn't block a spell like Banshee Veil does, it gives a lot more magic resistance and Banshee Veil's shield can be popped by any spell. An ad carry could just cast a random spell to pop your banshee and the AP carry will make fun of you

Mystic Shot must be taken at level 1 as it allows some good Harras. E is taken at level 2 to have a way to escape. It's nearly impossible to gank you with E, Flash and Ghost !
I maximise ultimate first, then my Q, my E and my W last (but I take 1 level at level 4)

The advantages of this build are :
-The capped CDR gives you great mobility aswell makes you a true Machine-gun that spams spells
-High damage ultimate
-Uses his skills to their maximum potiential
-Good escaping, chasin and kitting potential
-Strong early game (AD)
-Stong late game (AP)
-Nearly impossible to gank except if the ganker is a Kassadin

As an Ezreal, your role is to open the fight with your ultimate, flash next to the enemy carry, slows his attacks speed and unleash your burst , then autoattacks 2-3 times until he dies then your can ever continue by attacking the next squishy or blink out if you got focused.
Try to inform your team when you get level 6 so they can tell you when someone is sticking a tower with 10 HP

Ezreal is not a very good farmer but you can use his Q to farm.
If you are good at last-hitting then you don't need to waste Q to last-hit but you should use it to harass your opponent and zone them out.
You have a strong early, use that to your advantage to get fed.

Please note that this is my first guide and that I'm not good at english. If you have suggestions to help me improve this guide or if you spot some grammar errors please post a comment.
Thank you