Ap Ezreal is good bust champion which can really pack a lot of damage if built correctly. This guide will help teach the most effective build in your hope to carry your team in game.

I chose the magic penetration marks so you can burst down your opponent even further by disregarding the opponents MR
Magic resist glyphs are more important than armor, unless you are facing an ad mid.
Mana regen is very important with ezreal because to do any damage, you'll need to spam your abilities as mush as possible. Mana on Ap Ezreal is necessary, so until you get blue buff, mana regen is really necessary for early game.
No explanation needed for this choice of quint.

A pretty basic Ap mastery tree besides the attack damage and attack speed. i go 4 points in AD and Attack speed because with the combination of Lich Bane and EZ's passive, your Basic Attaks can hit hard as well in 1v1 fights or team fights.

This will help EZ burst and enemy down quickly and its passive helps do extra damage when all abilities are on CD
AP Ezreal is a mana heavy mid and the combination of mana and AP this item provides gives Ezreal a huge advantage.
This item is self-explanatory.
This item gives ezreal more lasting ability in teamfights and also provides a lot of Ap for Ezreal to do even more damage.
This item helps Ezreal kill the tankier members of the enemy team and shred their carries even more.The reason i choose CD boots is because Ezreal abilities are his only damage tactic, so the lower the cooldown, the more damage Ezreal can do.

This Ability is not only useful in killing enemies, but it is also a way of zoning opponents in lane and farming when Ez is being beaten in lane.
The reason i max W second is because it's ap ratio is very high and this skill will do the most damage in mid and late game.
Although this ability scales with Ap, it doesn't hit as hard as W so its necessary to grab a point early on for escape and then max it last.