AP/AD Hybrid is a pretty tricky mechanic, but Varus really is the perfect champ for it. His Q scales wonderfully with AD, dealing upward of 500 damage in a line late game. This works even better when paired with W, which adds magic damage as % of the target's max health, and scales off AP. He has very reliable damage for single-target and AOE, can carry a teamfight from a distance, and has an ult that can easily mess up half the enemy team if used right. It's also very hard to build against hybrid. Most tanks will lean heavily toward one or the other; few can properly defend against both types of damage, so you can play it smart and exploit any and all weaknesses.

This is where it gets tricky. I've tried this a couple different ways, some work pretty good, others not so much. One thing I can say for sure is DO NOT START WITH NASHOR'S TOOTH. Until you finish the build you'll be sitting at 30 AP, which means close enough to nothing for you. Going for Lich Bane first could work, depending on the situation, but in my experience, the most reliable course is to play it save and farm minions to build up Guinsoo's Rageblade ASAP. The Recurve Bow passive adds to the bonus damage from your W, and you hit a little harder with each progressive attack. Varus wants to hit someone at least three times to stack up his W.
Once you have Guinsoo's Rageblade and Berserker's Greaves, build into Lich Bane right away. That extra movement speed from Aether Wisp, small as it is, goes along with the boots to make you just a little faster than most others. This will help you keep at the edge of poking range, right where you wanna be. The key to Lich Bane on this build is to alternate between basic attacks and abilities. Each ability you use will proc the Sheen passive, so your next basic will do massive bonus damage. Then when you get three stacks of blight on the target, throw an ability at them. Around the time I finish Lich Bane I usually do around 8% of their max as bonus damage per stack, which along with ability damage itself can drop most champs about half their health with a fully charged Q.
Whether you build Gunblade or Rabadon's next is pretty dependant on the situation. If you find yourself having to use your R to lock people down so you can rain down on them, go for Rabadon's. The massive AP bonus will make your ultimate ridiculous. I've seen a 1700 damage ult at 3 Blight stacks after Rabadon's. If you're more dependent on your Q to catch someone at a distance, though, Gunblade's extra AD will definitely help. Whichever you build, take the other next.
Finish with Nashor's Tooth. If the game even goes this long, you'll need the extra CDR and attack speed.

I always start with Q because I like being able to poke at a distance, disturbing my opponent's early minion farm while adding to my own. The next two should be into W, in case your opponent tries to push hard. Do your best to stay out of their range and poke with basics. If they're foolish enough to let you get three stacks on them, punish them hard with Q. Take E at 5. If timed right, you can actually launch the volley, and get a basic in to apply an extra stack before it hits. *This takes practice and precision.* It's also a decent ability for zoning and throwing off a chase. Take your ult at 6, obviously, and then the fun begins. At this point, your focus should be to poke with three basics, then hit them with R for massive damage. While they're rooted, hit them again. They'll probably be free around the time of your third hit, but that's not a problem. A fully charged and well-aimed Q at three stacks of Blight will finish most champs at that point.