Hello this is Bolter778 and this is my guide to hybrid . In my opinion, I think that full out AD or AP does not bring out his true power meaning that some of his abilities scale on AP and AD so hybrid is a very good choice on .

Pros

-Has a natural flash Arcane Shift
-Team steroid Essence Flux
-Good Damage output
-Somewhat good skill set

Cons

-No Crowd control
-Squishy Exhaust or stun probably means death
-Difficult to master because his abilities are all skill shots
-Item dependent

So, the items are basic. The early Sheen then the Ionian Boots of Lucidity lets you have mana little AP, cool down reduction, and importantly, movement speed which gives you some flexibility, damage and a chance to spam your skills(not by a lot but it helps a lot).
Then, the Vampiric Scepter gives you a sustain and the Blasting Wand gives you more AP(more damage with skills).
Next, the Bilgewater Cutlass gives you more damage and sustain while the Pickaxe and the Guinsoo's Rageblade gives you hybrid damage which is useful early to mid game.
As you get into late game, flexibility and damage is an important factor. Therefore, the Lich Bane, which gives you more AP, Mana and movement speed, helps you a lot in team fights because you will need to sustain yourself and keep dealing damage. Also, the Alacrity Enchancement gives you more movement speed and that is helpful since Ezreal's movement speed is pretty low and he needs positioning.
Leading to late game, the Glacial Shroud helps with more survivability since it gives you armor. Then, the B. F. Sword, soon leading to a Mercurial Scimitar, Gives you more damage and survivability. The Iceborn Gauntlet helps you secure kills by slowing the enemy and since it gives armor, coodown reduction, and mana is a great item of choice.
Lastly, the Hextech Gunblade finishes the build, giving spell vamp and more hybrid damage.

For runes, get the Greater Seal of Armor and the Greater Glyph of Magic Resist since that makes you less squishy. Then, take Greater Mark of Hybrid Penetration and Greater Quintessence of Attack Damage for more damage.

Greater Seal of Armor
Greater Glyph of Magic Resist
Greater Mark of Hybrid Penetration Greater Mark of Hybrid Penetration
Greater Quintessence of Attack Damage

For Masteries take 21/9/0. The 21 on offense for obviously damage, and 9 on defense for more defense.

Rising Spell Force (Innate)- Hitting a target with any of Ezreal's abilities increases his attack speed by 10% for 6 seconds, stacking up to 5 times. Thanks to this spell we can focus more on attack damage items instead of attack speed. This ability stacks up to 5 times. You gain 5 Stacks after casting Trueshot Barrage.

Mystic Shot (Q)- Ezreal fires a bolt of energy that deals 35 / 55 / 75 / 95 / 115 (+1.0 per attack damage) (+20% of ability power) physical damage and applies on-hit effects. If it strikes an enemy unit it reduces all of Ezreal's cooldowns by 1 second. Your main ability, it's nowadays on a low CD and a low mana cost at all levels.

Essence Flux (W)- Ezreal fires a fluctuating wave of energy at a targeted area. Any enemy champions it passes through take 70 / 115 / 160 / 205 / 250 (+80% of ability power) magic damage, while any allied champions it travels through have their attack speed increased by 20 / 25 / 30 / 35 / 40 % for 5 seconds. Don't spam it, it has a very high manacost.

Arcane Shift (E)- Ezreal teleports to a target nearby location and fires a homing arrow at the nearest enemy unit dealing 75 / 125 / 175 / 225 / 275 (+75% of ability power) magic damage. A truly epic spell that will save you from certain death multiple times, if used wisely. Has a pretty long cooldown so only use it when you absolutely need it.

Trueshot Barrage (R)- Ezreal channels for 1 second to fire a powerful barrage of energy missiles, which deal 350 / 500 / 650 (+1.0 per bonus attack damage) (+90% of ability power) magic damage to each enemy unit they pass through. However, it deals 8% less damage for each additional unit it hits (30% minimum damage). Useful ultimate, global. Remember to use in beginning of teamfights and not to ks kills.

Mystic Shot (Q): Take it at level 1, 3, 5, 12 and 13. It deals the most damage of all your basic spells and applies on-hit effect for massive Life-Steal or damage by Sheen. It also reduces cooldowns while it still has a low cooldown.

Essence Flux (W): I Take it at level 4, 7, 8, 9, 10. This is useful in team fights as a steroid or a part of your combo as it passes through minions and damages champions.

Arcane Shift (E): Your escape/chase spell. Take it at level 2 and max it third. You also get it at level 14, 15, 17, and 18.

Trueshot Barrage (R): The ultimate skill of Ezreal! As it's your ultimate you max it first and you ALWAYS get it at level 6, 11 and maxing it at level 16. This is really the signature of Ezreal.

The reason for this is on early games, the Mystic Shot is a great poke and a point in Arcane Shift is useful for chasing and escaping. The points in Essence Flux at level 7, 8, 9, 10 are for mid game as there will be a lot of team fights at a lane. Since Essence Flux goes through minions and hits champions it is very useful at mid game. The reason why there are only 3 points in Mystic Shot is because it has a low cooldown even and has enough damage when it is level 3 and Essence Flux is very useful since it can go through minions to poke/hit enemies while Mystic Shot needs positioning. The reason why Arcane Shift is last is because it is mainly used as a Flash mechanic and you don't really need it as a damage source therefore you keep it as a utility spell.

80 CS - 10:00
100 CS - 15:00
150 CS - 20:00
200 CS - 30:00 (Now you should head up to fight teamfights and dragon, therefore you will most often lose some farms).
Aim usually for about that amount.
CS=Creep Score(Last Hit)

Flash provides you with a good escape and chase with your E Arcane Shift

Ignite is standard for add/fighters to finish off enemies or to secure the kill

Other Viable Options

Ghost is a viable replacement for Flash as you can use it to escape or chase

Exhaust is a viable replacement for Ignite because you can use it to prevent them from dealing much damage and to prevent their escape