Now, to start off, you never see a Drow in high-tier or professional games, and there's a reason for it. Drow is a easy kill, DPS hero with an amazing slow ability as well as a Silence. This exceptional skilled hero comes with two passives that increase her raw damage. This makes for a surprisingly easy to play with hero, but she is very weak and dies quickly.
Sadly, she gets played a lot, according to Dotabuff. Most chosen hero in public games. Now, we as the average player will cringe when we have to face this annoying hero in the throes of battle, as we don't know how to deal with heroes like her that are generally considered (by the less pro people) as a 'noob' hero. But really, its a new-player hero. It comes with only 1 real skill, an autocast, and fairly easy way to kill. But, the reason why this hero never comes up in pro games is simple; Drow Ranger is easy to counter. So playing in high-tier CM games will of course never offer up the Drow as a carry, because of how easy she is to kill...if you know how.
But, down here in mid-tier, we struggle with her. One guy accidently dies to her twice, and very often its over. And there's very seldom someone that counter-picks to take her out. The same goes for other heroes of the same caliber, such as Riki, Ursa etc.
What tips can I give to you when you face a Drow Ranger in combat? Mobility. Drow Ranger is a very squishy hero that gives in quickly. The ability to approach her instantly (such as blinking or using invisibility) is a fairly sure-fire way to take her out. If she has a Shadow Blade, there's always wards, dust and gems. Just like Riki, countering her strength brings you victory.
In conclusion, fighting those easy to play heroes is just a matter of practice. I daresay, playing with them will help you realize how to counter them.
So if you have to fight the feared Drow Ranger in combat, just exploit her weakness, very, very squisyness.
Riki and Sniper are also kinda anoying as well,l but at least for me they aint much mroe of a problem, some wards and a true sight usualy do the job and purification makes a really nice pure damadge.
I guess there's no best way to kill her, you just need to know(or predict) how she's going after you and then plan a little bit ahead, one sucessful in the early game or not letting her kill/farm too much will make her useless during the battle, it's at least what i do.
Now that I think about it, they are valid counters to Drow Ranger, too: multiple units (both Lone Druid and Meepo should work), built-in slows or disables like Unstable Current or Spiked Carapace and single-target disables like Astral Imprisonment, Disruption or Nightmare really help against her Frost Arrows.
Returning on topic, you can counter Drow Ranger with those OP Heroes we see in tournaments: Gyrocopter, Magnus and Dark Seer can easily target Drow with their ultimates (except for Seer, but he can escape from the arrows anyway) or initiate a fight with her in it; Batrider and Nyx Assassin, with the right item build, will have no difficulty while trying to deal with her. Plus, Phantom Lancer outcarries her by a long shot.
Otherwise, you can go with the usual dual-mid lane with Io and Chaos Knight/ Tiny/ Sven/ Dragon Knight: in the laning phase you won't let Drow farm and will occasionally kill her, in the mid game just get a Gem of True Sight or Dust of Appearance and you can gank her globally.
While I agree with your general line of thought, the reason she does not get picked in CM is because she is not in the pool and plain out overpowered. If drow would be in the pool we would actually see a lot of her. Even in pro games.
No you would not, she's been in the pool prior, she hasn't had any dramatic overhauls and she's definitely not over powered. She's a pub stomper, all the heroes to counter her are not popular pub picks, that's why she's so easy to play.