Varus is a very underrated AD carry in the NA scene, he is a more DOTA style type of semi-carry with a ridiculous utility kit of CC. What I mean by DOTA style of play is where, you poke them out and then when you poke them low enough you go all in for the kill.
Varus excels at that type of play more than other AD carries besides Caitlyn. He has the best team-fight presence out of all the other AD carries because of his ultimate that roots one target and has the chance to spread to the rest of the enemy team and root them. Having other champions on your team with similar AoE ultimates such as Orianna or Amumu, makes Varus synergize well with AoE teamcomps.
Pros & Cons
+Hard CC that chains very well into AoE CC
+High early and mid game damage
+Mixed damage types (physical and magical) yet with decent AD scaling
+Initiate ability (though not anything close to Ashe's)
+Strong at pushing minions and towers with his passive
+High base movement speed (310 when AD carries usually have 300 or 305)
+Combination of both decent burst and good DPS
-Lesser amounts of damage late game than some other AD carries (Tristana, Vayne)
-Mana dependent for damage
Beginning the laning phase, you want to start getting free poke hits as soon as possible. Always take the free hits that the enemy bot lane gives you where they can't attack you back. But at the same time do your best to get as much CS as possible, making them miss a CS is always good no matter what, but if you can make them miss a CS, while poking and getting CS yourself, that's even better.
When playing Varus try a few moves to start out... poke them when they go in to get a caster creep CS, and poke them when they come to poke you and mainly focus on your CSing except when those two situations occur.
Getting ahead of the enemy AD carry is key to winning your lane, zoning them is even better. Varus has great range to even poke them as they try to tower CS also, pushing early isn't bad but only do it when you know a jungler is going to do a regular jungle route and not gank bot level 2, like an Amumu/Nautilus/Mundo/Nocturne.
Having a early ward set-up in river helps too to know when you can be aggressive and when you can't.
As you practice more and more Varus you'll get use to his playstyle and abuse his poking range.
Mid/Late Game is where Varus shines. Whenever you pick Varus you would hope that your teammates picked champions with CC also such as Leona/Taric/Alistar/Annie/Morgana/Nautilus/Riven etc... in any given teamfight you want to look for any pick-offs with your ultimate onto either their AP carry or their AD carry, catching any one of them is a good situation for your team and allows them to followup with stuns to burst them down instantly. Varus has great initiation with his ultimate and great escape.
If that doesn't happen save your ultimate for when they clump up or a bruiser is running directly at you and noone is stopping him. When you land an ultimate as they clump up it is always wise you throw your E ontop of them right afterwards to prevent any healing they do as your team begins to chop them up.
Varus is a snowballing type-champion in a teamfight, as soon as the first person dies that you were apart of is where he becomes one of the best AD carries in the game, that attack speed passive is an amazing skill for any AD carry.
While also having the ability to use your Q to snipe off runners or providing huge burst on one target after getting your 3-hit W ability onto them is great.
Never dive in after any AP carry or AD carry in any given teamfight, always let them come to you or attack the closest thing next to you.... you don't want to be put into a bad position where the enemy team can turn on you and gib you instantly, that's what they want you to do.
AD carries are meant to tear through the opposing teams front-line, having one of their carries come close to you is like Christmas. If their carries are in a bad-position that's when you target them, if not mow through their front-line until an opportunity to take out a carry arises. Never forgo your positioning as an AD carry to dive someone unless you have a great team-comp with CC to back you up.