The Greater Mark of Desolation will allow more damage to be dealt to enemy champions when basic attacks become the main damage source during mid-game and late game.
The Greater Seal of Clarity is not going to be as useful early game as it will be late game, because it starts off with low mana regeneration but will build up more as you level. As leveling proceeds, your mana regeneration will increase, allowing more harassing to occur, since your mana won't need to be saved as much because the regeneration will be so fast.
The Greater Glyph of Focus is going to allow you to spam Mystic Shot a bit faster to harass and to farm well. If Mystic Shot hits, its cooldown will be reduced by one second, which will allow for even more spamming.
The Greater Quintessence of Strength will allow the early game Mystic Shot harassment to do more damage to the opposing team champions. Farming will become much easier with the extra attack when using basic attacks and Mystic Shot. During the mid-game and late game stages when skills become less of a necessity, besides mainly Arcane Shift and Trueshot Barrage, you can do even more damage with basic attacks, which will become the main source of damage.

Doran's Blade- Will give Ezreal more sustainability in lane from the life steal and extra health. Will allow more harassment with Mystic Shot because of the addition attack.
Sword of the Occult- Getting kills when having Sword of the Occult will give him more damage early game with Mystic Shot harassment and deadly mid-game/late game damage with basic attacks and Trueshot Barrage. When Sword of the Occult has full stacks, Ezreal will get additional movement speed, which is a necessity when playing Ezreal because of his slow movement speed.
Boots of Swiftness- This item is an extreme necessity early game to escape ganks and lost fights more easily. However, if the build is completed, Ezreal's movement speed will be so great that you can possibly switch it out with Phantom Dancer or Berserker's Greaves for additional attack speed.
The Bloodthirster- First of all, getting stacks on this item should be extremely easy, and you may just want to rush it first or after Sword of the Occult. Additional attack from this item will give more damage output in team fights and will allow farming to become much easier, if the team fight stage hasn't started. If you manage to get this item early game, the Mystic Shot harassment will become extremely deadly. The life steal will become extremely helpful. If you are ignited and nearly dead, simply go into the jungle and slowly regain health. 1 vs 1 fights will be much easier for you; while your enemy is getting lower in health from the great damage output, your life will barely get lower.
Phantom Dancer- Attack speed, critical, and movement speed are all extremely useful on Ezreal. Movement speed will help you gank enemies more and be a useful carry. Attack speed and critical hits, alongside a fully stacked The Bloodthirster, will allow heath regeneration to happen faster and with more life gain from possible critical hits.
Infinity Edge- This item gives quite a bit of attack which will help with late game damage output with basic attacks and skills, especially with Trueshot Barrage. The critical hits' increased damage will be helpful in team fights.
Trinity Force- Trinity Force adds mana and health, which is needed a lot with Ezreal. More health will allow Ezreal to last longer in team fights, which is your main concern, because it should be the team fighting stage when this item is obtained. The mana will allow skills to be spammed, which will activate the Sheen part of Trinity Force. The Sheen allows the next basic attack to deal 150% damage. The additional movement speed won't be as needed with the great amount of movement speed that should have already been acquired, but it still will be a great escape method. Basic attacks will have a chance to slow targeted enemy, and since your attack speed will be extremely fast, you are almost guaranteed to slow enemies.

The first skill that you really want to max first is Mystic Shot. Seeing how this skill is going to be your most used skill throughout the game, having it maxed first during team fights is going to be really necessary. During the laning/farming stage, Mystic Shot is going to come in handy with last hitting minions and harassing enemy champions. This skill will also be used more often to trigger Ezreal's attack speed passive ability.
The next skill that you are going to extremely want to max is Arcane Shift. Arcane Shift is the most useful throughout the game. Since it will be used to escape or chase down enemies, you are really going to want it to have as minimal cooldown as possible.
The third skill that you will want to max is Ezreal's ultimate ability: Trueshot Barrage. This skill will be helpful in the beginning of team fights to start it off with a huge damage output. When laning, you are going to have to be aware of the other lanes to kill enemies that are overstaying their welcome.
The final ability that you are going to max is Essence Flux. During team fights, Essence Flux could come in handy because of its ability to slow an enemy's attack speed and increasing an ally's attack speed. This skill will also be helpful with harassment during the laning stage. Mystic Shot should be used more for harassment, because it scales off attack damage more than Essence Flux, and Essence Flux scales off ability power. However, seeing how this ability only hits champions, it can almost be a guaranteed hit.

First thing that must be said: FARMING IS A MUST.

Farming on any attack damage carry is extremely needed. With this build, you are going to need the last hits on minions because of the costly items. Luckily, Ezreal is a reall good farmer; his basic attacks are strong enough to last hit minions when they have a bit of health left, and Mystic Shot will do enough damage to kill minions from one-third health early on.

If farmed well, you will reach the full potential of Ezreal's power with this build.

Early game when Ezreal is at his squishiest and slowest, Ghost will become extremely helpful from ganks from junglers and other teammates. Later in the game, Ghost will only become useful when trying to escape from a losing team fight, trying to chase down fleeing enemies with low health, or going to the aid of a falling turret.
Ignite is one of the most useful summoner skill. Ezreal is an excellent harasser early game with Mystic Shot. During a little scuffle against an enemy, if you get them extremely low, Ignite will come in handy for the final blow and could help get stacks on Sword of the Occult.

Pros

Great early game harasser
Will be a quick moving carry
Great escape (from Arcane Shift and speed)
Mid-game/late game killer
Great damage output
Awesome farmer

Cons

Extremely squishy
Slow movement in the beginning
Cannot spam skills as much until late game, when basic attacks become the main damage output
Extremely hard to play because of only skill shot attacks