This is a fairly simplistic AD Carry build for Ez. I do think that an AP Ez build is viable but its based on burst damage and is too inconsistent.

First off there are a few key things you need to know:

Ez is squishy, deal with it.
Ez has mostly short range attacks, with a mother huge long range attack.
Ez needs a team to back him up. He is great darting in and out but will die going toe to toe.
Ez has both AD and AP attacks, pick which way you want to go and stick with it.

If you want an in depth rundown on skills, mastery, and runes check out Booshido's Guide to AD Ez. I agree with 90% of his methods and used some of his concepts here.

The items should be self explanatory for the most part.

Variations would be to add in Banshee's Veil or Thornmail after Trinity Force to counter what your getting hit by. Usually this would not be recommended but if you are just starting out and finding AP or AD heavy matches, pick the one that helps.

This is where things tend to get debated a lot so lets look at things in three different scenarios, laning, 1v1 and Team Fights.

Laning
Ez is not a particularly strong at laning early on. He has the potential to build gold quickly by using Mystic Shot to get the last hit.

Do not push with Ez as he will get ganked easily until you are level 4-6 and have Sheen.

Current meta seems to like Ez at bottom, or in certain cases middle if he has jungler support to set traps.

1v1's
Ez is a good 1v1 champ dependant on what your fighting. If your opponent can quickly close the gap like Yi or Zin you are going to get into some serious trouble. If you have been working on your TriForce and already have your Phage you should be able to use Arcane Shift to keep ahead of your opponent and kite him till death.

Your skill sequence will not be fixed but should heavily focus on using Mystic Shot as your opener, then Essence Flux to reduce enemy attack speed. Use Arcane Shift where needed to keep your distance.

You have two options for your TrueShot Barrage, either use it to kill the runners from a 1v1, or use it to initiate by hitting minions and trying to clip your opponent(to max your attack speed bonus at 50% and do a little damage). This isn't your big killer as your not in an AP build.

Team Fights
Never initiate a team fight with Ez, he does not have the survivability required. Avoid using Arcane Shift to get into the fight unless you are sure you wont draw focus, or get killed in area effects.

Now, what Ez does do well in a fight is assassinate players that are on the fringes or vulnerable.

Use Trueshot Barrage at the start of a fight. Ignore the wailing of people that dont understand the mechanics of the build. If you dont use it at the start you have two problems. The first is your most powerful attack, Mystic Shot, will hit minions not Champions unless you clear them. The second is you are missing out on a 50% attack speed increase for your now punishing auto attack.

Throw large amounts of Mystic Shot and alternate with Essence Flux every 3-4 shot. Essence flux should be aimed at YOUR champions where possible. It will likely hit the opponents anyway but you want to make sure your champions are getting the 40% attack speed bonus rather than deny the opponent attack speed.

Use Arcane Shift to avoid effects, keep out of the battle, and to close in on wounded champions trying to escape the middle. DO NOT CHASE, if an opposing champion flees a team battle stick with your team unless he is the last or second to last champion remaining.