This build is mainly offensive, meaning if you take solo, you should play somewhat conservatively early to mid game, until you feel yourself becoming really powerful. You'll know what i'm saying. :]

Pros
-Insane burst damage
-Spammable skills
-Destroys tanks

Cons
-VERY squishy
-High mana cost early game
-Costly to build

Greater Mark of Desolation - Armor pen. Helps damage output.
Greater Seal of Focus - Cooldown reduction. Helps skills becoming spammable.
Greater Glyph of Focus - Same as above.
Greater Quintessence of Desolation - More armor pen.

The offense is obviously to increase damage output, and make your burst damage overpowering. The defensive bonuses are enough to keep you in lane early game.

I rush manamune always, this helps with my build tremendously. I do, however, get boots of speed right before I buy the manamune itself. This helps your mana stay up while laning, so when a fight starts, you have the necessary mana to burst them dead. I then buy a vampiric sceptre to help with laning and survivability, then a dagger for the slight attack speed. I then buy a BF sword to then finish off the black cleaver. With your 31 starting armor pen, and the abilites of the cleaver, tankier enemies will quickly be smashed in teamfights. I then buy another BF sword to make a bloodthirster. if possible, STAY ALIVE FROM NOW ON. The stacks built onto this will tremendously increase survivability and damage output. Next, buy a pickaxe, then another BF sword and get the remaining 1205 gold to build your infinity edge. At this point, you're hitting easy 1k+ with crits, not to mention abilities being spammed. When building your last item, Madred's bloodrazors, I suggest buying the recurve bow first, to increase damage output with your crits.

Your priority should always be this:
Trueshot Barrage > Mystic Shot > Essence Flux > Arcane Shift
I'd make sure your first two abilites are leveled as much as possible because your first reduces cooldowns, and your second goes through minions, as well as lowering/buffing other champions attack speed. The exception is made at level 2, because arcane shift is completely necessary for getting away/chasing kills.

Flash and ghost. Always. As squishy as Ezreal is, these are both used to get away multiple times per game, and WILL save you. Flash + arcane shift together can make you jump a complete screen length in a half second.

Thanks for reading, hope this helps. Comment with any questions or problems you see. I take criticism as a way to better my guide and/or myself as a player, so it's encouraged.