Ezreal is a ranged champion, a good solo champ if it is well played can also be an helper of the team.
And his ulti is prety good to assist the at long distances and clean minion waves.

PROS:
Good demage at long range
personal flash
can give atack speed to your mates
checker
CONS:
Squishy
first being targeted
little weak vs tanks

Greater mark of desolation ok some people think ezreal is only ability power but they are wrong his first ability does atack demage, this can increase the demage of this skill.
Geater glyph of potency Ezreal is build with atack demage and ability power this runes increase increase a lot your ulti and your first skill because they are hybrid.
Greater seals of Replenishment even with the utilty build you need this runes to get a good regen.
Greater Quintences of desolation I recomend this one because this runes improve yout main ability even more than the marks.

9/0/21 why?
You can do 21/0/9 its fine but you will be out of mana in a sec.
If use perseverence and meditation you get a good mana regeneration.Use haste to improve your ghost and and presence of the master to keep your summoner spells up more quicly.Now the most important on the utility tree Expanded mind this mastery gives you more 5% of mana, why is so good? Simple, if you got more mana you will receive more AP and AD from Manamune and Archangel Staff.
Finaly the Ofense tree you should use at least the archaic knowledge to get some magic pen.

Start with doran´s blade to 3vs3, use vampiric scepter to 5v5 when you reach you reach late you can sell it on the store you need that to get some life at start.
Buy Manamune and just than buy Archangel staff Atack power is better to your main skill, if you buy this items you in late game you will have 4000 of mana an awesome regen.
Ezreal is a little squishy so buy some defensive items like Banshees veil, try always to buy items with mana because with more mana you will gain more AP and AD.
And Finaly buy Rylai´s crystal scepter or Frozen malet to get some health and aplie slow on the enemies.

First learn Mystic Shot (your main skill) to check the bushes and get some good long range demage, than learn Arcane Shift to teleport away from the battle or reach the enemy if necessary and at last learn Essence Flux, this skill ignores minions, wich means that it only hits champions, when it hits a enemy champion it decreases its attack speed and gives him damage, when hit your Allies it increases their attack speed significantly and it is very good in group fights and in tower destruction.
TrueShot Barrage this skill is hybrid combines you AP and AD and releases a power full wave of energy that travel demaging all the enemies on his way.

To 3vs3 take Ghost and Exhaust.Now I will explain you ghost and not flash, thats simple you got a personal flash you dont need another one you can already cross walls with arcane shift.
To 5v5 take Ghost and teleport, I use teleport dont let my enemy hit the tower but you can take exhaust or ignite but i recomend you this I think is more apropriate.

So Ezreal lots of times is use to solo, his squishy and a good demage dealer so if you got a friend prepared to gank just go you will probaly kill him.
Another thing never walk alone it could be a large error.
And finaly and most important int he fight try to stay back giving skill shots, dont ever let an enenmy reach you so stay behind but atacking.
Have fun playing and dont forget to vote.

5lyk