This is my style of playing Ezreal.Some things on this build are inspired from the Chauster's Ezreal guide found here.

Pros

Perfect Mid.
Spammable skills.
Great escape.
Great early game Nuke.
Usefull Ult.
Sexy skill animations.
Best dance in the game.


Cons

Squishy!
No CC!
Vulnerable to CC.
Targeted first.
Some difiiculty to master.
Slight mana issues.

Marks: Armor penetration
Seals: MP5 per lvl
Glyphs: MP5 per lvl
Quints: Attack damage

Marks-ArP for players who will be stacking armor
Seals&Glyphs-You'll have mana problems without the blue buff
Quints-Extra AD doesn't hurts

15/0/15 is the best mastery set for Ezreal.Good AD and ArP while having some utility late game(Mystic Shot)

Early game:Buy two Doran's Blades for lane sustainbility.The Brutalizer for extra damage and ArP.Boots:Here you'll have to make a choice.If the enemy team has a lot of CC's take Mercury's Treads.If the game goes well take Ionian's Boots of Lucidity.If you're laning against an AD carry that does a lot of damage take Ninja Tabi.

Mid game:Here you'll have to make a choice:If the game goes well and you're getting kills take The Bloodthirster>Last Whisperer.If the game doesn't go that well(it shouldn't go bad)go for Infinity Edge>Last whisperer.

Late Game:Sell a Doran's Blade to make room for Phage.After that finish Trinity Force.If you finished Trinity Force kepp your money for a Frozen Mallet then sell your other Blade(+10 damage and +500 -3% lifesteal)

Passive: Rising Spell Force

Hitting a target with any of Ezreal's abilities increases his attack speed by 10% for 6 seconds (Max Stacks: 5).

Explanation:


Ezreal's passive is great during team fights as a well timed ultimate will allow Ezreal to have maxed attack speed stacks. This passive is pretty useless in lane as Ezreal rarely spams auto attacks in lane as he will lose the exchange due to his low range and increased change of taking minion aggro. Also, to stack a significant amount of his passive would require an excessive amount of mana, which would be better utilized with proper spell usage. When trying to DPS turrets, try to get stacks from mystic shots or use your ultimate to hit creeps down the lane.


Q: Mystic Shot

Ezreal fires a bolt of energy dealing 40 / 65 / 90 / 115 / 140 plus 110% of his attack damage as physical damage (applies on-hit effects).

Ezreal's cooldowns are reduced by 1 second if Mystic Shot hits a target.

Cost 30 / 35 / 40 / 45 / 50mana
Range 10000

Explanation:


Ezreal's bread and butter skill. Use this spell to harass champions in lane and team fights. Most people forget that spamming mystic shot actually lowers cool down. A common situation where this is crucial is during small skirmishes where you have used arcane shift and are kiting an enemy who is ghosted. Instead of blindly running away (you aren't getting away on foot anyways) spam mystic shot on targets to get back arcane shift cooldown (while running of course).

W: Essence Flux

Ezreal fires a wave of energy that damages all enemy champions it passes through for 75 / 125 / 175 / 225 / 275 (+60% of ability power). Affected ally and enemy champions have their attack speed respectively hasted or slowed by 20 / 25 / 30 / 35 / 40% for 5 seconds.

Cost 80 / 90 / 100 / 110 / 120mana
Range 10000

Explanation:


Ezreal is played as AD nowadays so this spell is essentially worthless. You can use this in team fights for some added damage if you have the mana to support it, otherwise save it for when you can cast it on enemy DPS to slow attack speed.

E: Arcane Shift

Ezreal teleports to a target nearby location and fires a homing arrow at the nearest enemy unit dealing 80 / 130 / 180 / 230 / 280 (+75% of ability power) magic damage.

Cost 90mana
Range 10000

Explanation:


Arcane shift allows Ezreal to play incredibly aggressive during the laning phase. You can arcane shift offensively for better mystic shot placements or even to get surprise auto attacks. A common mistake Ezreal users will do is use arcane shift to maximize distance away from enemy pursuers. The best means of escape will almost always be to shift over a wall.


R: Trueshot Barrage

Ezreal channels for 1 second to fire a barrage of missiles dealing 350 / 500 / 650 (+70% of ability power, +1 per bonus attack damage) magic damage to each unit it passes through. However, it deals 8% less damage for each unit it hits (Minimum 30%).

Cost 150mana
Range 20000

Explanation:



Ezreal's ultimate is great for initiating ganks or to burst down unsuspecting champions in lane. During lane phase, walk out of the enemy's line of sight in order to cast your ultimate to deal some serious burst damage. This allows you to farm more freely or even deny the enemy champion if their HP has dropped too low. In team fights, you should be maximizing the damage of the ultimate by using it when enemy champions line up. Obviously 5 champions will almost never line up, so if you think you can hit ~3 champions go ahead and shoot it. Do not use this ultimate to farm creep unless you are getting pushed hard or expect that no team fights/skirmishes will start for awhile.

Cleanse- Ezreal is extremely squishy. If you are caught out of position and CC'd you are as good as dead.

Flash- best summoner spell for all AD carries. This allows Ezreal to travel great distances with a dual blink or allow Ezreal to have amazing escape potential as he can kite over two walls.

These are the summoner spells I take as they fit my play style and I am very used to them. Other players can substitute ghost, ignite, and exhaust and mix the summoners as they please (ie. ghost + ignite, flash + ignite, ghost + cleanse, etc).