Varus is a Marksman who can perform well with many different builds. This build will cover the hybrid attack damage, attack speed, and ability power based build.

The main source of damage from this build is due to the on-hit effects from Guinsoo's passive, Runaan's Passive, and BoTRK's passive.

Pros

Great teamfights
Lane harass
Easy to farm with due to his W

Cons

No escapes
Not a reliable source of AP

Living Vengeance (Passive)

Varus gains 20% bonus attack speed for 3 seconds upon killing a minion or monster, increased to 40% bonus attack speed for 6 seconds upon taking down an enemy champion.

Piercing Arrow (Q)

First Cast: Varus channels for up to 4 seconds, increasing Piercing Arrow's range and damage over the next 2 seconds.
Second Cast: Varus fires, dealing physical damage to all enemies in the arrow's path, reduced by 15% per enemy hit down to a minimum of 33% damage.

Blighted Quiver (W)

Passive: Varus's basic attacks deal bonus magic damage and apply Blighted Quiver Blight for 6 seconds, stacking up to 3 times.
Varus's other abilities consume Blighted Quiver Blight on enemies upon damaging them, dealing them magic damage for each stack, capped at 360 against monsters.

Hail of Arrows (E)

Active: Varus fires a hail of arrows that deals physical damage to all enemies in the target area and desecrates the ground for 4 seconds, Slow icon slowing all enemies standing in it and applying Grievous Wounds icon grievous wounds.

Chain of Corruption (R)

Active: Varus flings out a tendril of corruption that infects the first enemy champion hit, dealing magic damage, Root icon rooting them for 2 seconds and applying 3 stacks of Blighted Quiver Blight.

The corruption then attempts to spread towards nearby enemy champions that stay near the infected champion for 2 seconds, applying the same effects, then continues to spread until there are no further targets in range. Each champion can only be infected once per cast.