I've heard a lot of trash talking on mid thresh. Let's set it straight.
You're gonna want to head to lane with a long sword and 2 hp pots. Stacking up your AD early game is essential to securing your kills and general lane harass. Like usual lane phase, focus on last hitting. Thresh's passive on his Q makes it nearly impossible to miss CS, and is also the sole reason Mid AD thresh is so powerful. Nearly every popular mid lane champ is squishy, meaning thresh's basic attacks will shred through enemy health. You're going to want to max your Q first, and try to pick up all souls dropped (The bonus magic damage is scaled off how many souls you've collected).
If you keep your harass up and play aggressively, you can get a kill at about level 3.
Things to look out for: Enemy jungler (obviously), High damaging ap champs (brand, veigar, lux).
Champs you're PROBABLY going to do terrible against: Diana, Well played Zyra, Vladmir, Aggressive lux.
Other tips: Just play somewhat aggressively, you're attack range is pretty long. Make sure they know you can deal a lot of damage and they'll sit back. Never let them initiate the fight first unless they have little to no damage. The point in your moves is to allow you to cc and initiate as you please. If you're struggling in lane, at level 6 you can almost guarantee a kill if you manage to pull them under your turret. Thresh has somewhat low mana usage, as long as you don't just needlessly spam your moves. Don't kill minion waves with your E, focus on using your moves on enemy mid.

Now, assuming you've played well, enemy mid should be shut down (or at least struggling).
By 20minutes into the game, you should have at LEAST Berzerker Greaves, Vampiric Scepter, and a Zeal. Most games you should easily have a BF sword, or even Bloodthirster at this point. Heres where the game picks up. With your higher damage now, focus on staying in 1v1 situations, don't take on multiple people unless they're weak-ish. Always pay close attention to your Q passive, when the icon hits red, you'll do close to your max bonus damage on your next basic attack. At this point, squishy champs like lux, fiddle, sona (most ap's if built with non tank items), should be taking heavy damage from your Q passive basic attacks. If they're below 600 hp, many times you can easily just 1hit them.
Once you build an infinity edge or phantom dancer (whichever you feel like building first), you can rely on your crits to do massive damage to enemies in just a couple hits. Every chance you get, keep farming up in lanes, jungle a little, roam to pick up those kills. Thresh snowballs easily if you've had a decent early game.

Pros:
Outrageous basic attack based burst
Best CC in the game (imo)
Passive armor and ap scaling, meaning you don't need ap items to do decent damage, and being naturally tanky.

Cons:
Can be counterpicked fairly easily (assuming they know HOW to counter him...)
No magic resist scaling, midding against ap's will be dangerous if you let them hit you.
Somewhat limited mobility.