Begin the game with a Ruby Crystal and your choice of a mana/health pot. Quickly turn it into a Catalyst for early game lane survivability and mana. After that build Sorc. Boots for magic pen, considering this is a mostly AP build, followed by a sheen which will later be built into a Lich Bane. After you get your sheen build guinsoo's this will allow you to maintain Ezreal's DPS in 1v1's as well as team fights capping his APS at ~1.4/sec end game. Once you have your guinsoo's turn your catalyst into banshee's, followed by building a bilgewater cutlass to give more survivablity in team fights, considering it will be mid-game by this point in the build and team fights will be frequent. Once you finish your gunblade you can either go straight for Rabadon's death cap for that extra ult damage. or you can finish your Lich bane for Q proc and pushing turrets. Once build is finished you will have approx. 400-500 AP and ~1.1k ult, as well as sustainability in team fights as well as solo fights.

*Note* I am well aware that i did not include anything about play style. Everyone has their own play style and you must account for that yourself when considering a build. I could easily tell you my play style, but that would not help you out in the slightest since, as i said, every1 has their own. My play style is more defensive harass early, followed by offensive nuke mid-late game.

Hope you enjoy this build.