Varus is the brand new AD carry and I would like to share two ways that I build him.
Please feel free to leave comments on how I can improve my guide. REMEMBER this is a guideline on how I like to play him. Try it a few times and mix the items up to your liking. Please try it out and leave a comment on how I can improve it. I want your opinion. Thank you for reading.

PROS
Huge range
Tons of cc for a carry
High damage
Percentage damage based on health
passive damage
passive attack speed increase

CONS
Squishy
No real escape
weak consistent damage early

Masteries I got 21-9-0. In offense I go the standard crit AD carry setup. In the defensive section i prefer a few points of armor or magic resist, but I mostly rely on this tree of the bonus health. The bonus health gives your carry just a little more to work with so he is not so squishy early.

-Piercing Arrow - Varus readies and then fires a powerful shot that gains extra range and damage the longer he spends preparing to fire.
First Cast: Varus starts drawing back his next shot, gradually increasing its range and damage.
Second Cast: Varus fires, dealing 10/43/77/110/143 (+1.0 AD) to 15/65/115/165/215 (+1.6 AD) physical damage, reduced by 15% per enemy hit (minimum 33%).

Piercing Arrow- is your main harass. Charging it gives you ridiculous range to harass or kill a fleeing enemy. Be warned though it has 2 casts or hold it on smart cast to charge it. You can move while charging but you will walk slower. If you hold it for 4 seconds after fully charged it will fail and you will get half the mana back. Be careful if your trying to kill someone that is running. Its damage goes down significantly for every enemy it hits so take your time to aim, and if you know your going to miss just hold it for the small mana refund.I would only max this first if you are with a Soraka or have blue buff all day because it takes tons of mana.

Blighted Quiver - Varus' basic attacks deal bonus magic damage and apply Blight. Varus' other abilities detonate Blight, dealing magic damage based on the target's maximum health.
Passive: Varus' basic attacks deal 10/14/18/22/26 (+0.25) bonus magic damage and apply Blight for 6 seconds (stacks 3 times).
Varus' other abilities detonate Blight, dealing magic damage equal to 2/2.75/3.5/4.25/5% (+0.01%) of the target's maximum Health per stack (Max: 360 total damage vs Monsters).
This ability is much like Twitch's poison stacks however, there is no damage over time and they are not detonated by this ability. To set them off you must hit with one of your other abilities. So land some basic attacks then use Piercing Arrow or Hail of Arrows.
Also this ability gives Varus passive magic damage to make up for his early low attack damage.

Hail of ArrowsHail of Arrows - Varus fires a hail of arrows that deal physical damage and desecrate the ground. Desecrated ground slows enemies' Movement Speed and reduces their healing and regeneration.
Varus fires a hail of arrows that deals 65/105/145/185/225 (+.6 bonus AD) physical damage and desecrates the ground for 4 seconds.
Desecrated Ground slows enemy Movement Speed by 25/30/35/40/45% and reduces healing effects by 50%.
This is pretty much a remake of Miss Fortune's Bullet Time. Varus fires a single wave of arrows that do a small to decent amount of damage, but it's effects are much more valuable.
Anything that walks through the area is slowed and loses 50% health regeneration rate and healing effects. So this skills is not only great to trap a champion, but it should be fired into the middle of the enemy team during a team fight to reduce their chances of regaining health.

Chain of Corruption (Ultimate) - Varus flings out a tendril of corruption that immobilizes the first enemy champion hit and then spreads towards nearby uninfected champions, immobilizing them too on contact.
Varus flings out a tendril of corruption that deals 150/250/350 (+1.0 ability power) and immobilizes the first enemy champion hit for 2 seconds.
The corruption then spreads towards nearby uninfected enemy champions, applying the same damage and immobilize if it reaches them.
Varus' ultimate has many uses. You can initiate when your team comes for a gank. Stop a fleeing enemy. Or pin an entire enemy team during a team fight. You must remember that this is another skill shot so take a second to aim and don't waste this amazing ult.

Living Vengeance (Passive) - On kill or assist, Varus temporarily gains Attack Speed. This bonus is larger if the enemy is a champion.
This passive is great. It helps farm minions early and gives a nice 20% bonus to attack speed to get in shots early on enemy champions. When you kill or get an assist in a team fight it makes varus super effective. You can a 40% bonus on attack speed to help finish the fight.

Varus is a ranged carry. That means stay behind your tanks in fights and try to kill everything that moves. Varus is great at harassing enemy champions. He can also tip the scales in a team fight pretty easily with his ult and E ability. Make sure you use all of his abilities wisely.

For his incomparable skill with the bow and his unquestioned sense of honor, Varus was chosen to be the warden of a sacred Ionian temple. The temple was built to contain an ancient pit of corruption so vile that Ionian Elders feared it could envelop the island in darkness. Varus prided himself on his position, as only the most exceptional Ionian warriors were selected for the role. He lived with his family in a nearby village and led a quiet life of disciplined routine until the day the forces of Noxus invaded Ionia. Their shock troops left nothing but death and desolation in their wake, and the temple lay in their path. Varus was forced to make a decision. He was bound by honor to stay and defend the temple, but without him the village's few inhabitants could offer little resistance against the oncoming war machine. Gravely, he chose to fulfill his duty as a warden. The corruption could not be allowed to escape.

His arrows sundered the troops who tried to wrest the temple from him that day. However, when he returned to his village, he found that it had been reduced to a smoldering graveyard. Remorse at the sight of his slain family gave way to overwhelming regret and then to seething hatred. He swore to slaughter every Noxian invader, but first he needed to become stronger. He turned to that which he had sacrificed everything to protect. The pit of corruption would consume him wholly, as a flame devours a wick, but its abominable power would burn within him until he was lost. This was a path from which there could be no return. With grim resolve, he condemned himself to the black flames, feeling malevolent energy bond to his skin... and with it, the promise of ruin. He left, seeking the blood of all Noxians involved with the invasion, a grisly task that eventually led him to the invasion's most infamous perpetrators in the League of Legends.

"The life of an arrow is fleeting, built of nothing but direction and intent."
- Varus, The Arrow of Retribution