Run Exhaust against teams with assassins such as Zed.

Items:
Relic Shield is the current meta starting item on Thresh, as he has an easy time last hitting with Flay passive, and it provides survival and sustain for trading.
Ancient Coin is sometimes an option, as it allows mana sustain, and early CDR for catching people out with unexpected Death Sentence casts. Also helps CDR cap faster, at the loss of tank stats.
Boots, Sightstone, and Oracle Lens are your early priority, with Control Wards mixed in for pressure and control.
Mobility Boots are high priority for mid-game pressure and roaming. Can help you run up on people and catch them out.
Redemption is the big priority first complete item on Thresh, for the tank stats it provides, and the fight-swinging active.
Locket of the Iron Solari synergizes well with Redemption. The active can keep people alive long enough for the Redemption heal to land, and the resists the item gives back up the health Redemption provides.
Face of the Mountain is a good item due to the CDR and health, and the active can turn scraps, and prevent targets from being bursted in fights.
Ruby Sightstone is an excellent item, as it provides substantial health, and allows the rest of your actives to come off cooldown more quickly.
Banner of Command is an acceptable item to build if you need more CDR and armor. It also provides some additional proxy lane pressure when you can't afford to send someone to split.
Eye of the Equinox and Eye of the Oasis are decent item options when fights are more spread out, and you're less likely to need the active CDR from Ruby Sightstone. They open up an item slot for later.
Talisman of Ascension is a good item to complete roughly 3rd, if your team is planning on playing around mobility.
Mikael's Blessing is a great item to build if the enemy team is crippling the kit of one or more of your team members with some form of CC, particularly stuns, taunts, and fears. It also takes care of 10% CDR.
Zz'Rot Portal is a great item to build for holding against siege, or applying proxy pressure later in the game. It also provides substantial resistances, which go well with the notable health Thresh usually gets from items.
Knight's Vow is a good item to pair late game, against low burst, high DPS teams.
Zeke's Harbinger is an incredibly aggressive item for Thresh. Only build this if snowballing. Particularly good on the Fervor of Battle build.
Ionian Boots of Lucidity: Build these if you can't leave your ADC alone safely.
Luxury: You'll rarely build these.
Dead Man's Plate: Great for catching people.
Warmog's Armor: Great for late game tankiness, if you're initiating fights a lot and still need CDR.
Randuin's Omen: Great if you're front-lining a lot against a crit heavy team.
Banshee's Veil: Budget Magic resist. Usually Locket of the Iron Solari is enough.
Gargoyle Stoneplate: Another good item if you're initiating fights by going in on Death Sentence. The new tank Guardian Angel.
Thornmail: A good luxury item if you're front-lining against auto attack heavy teams.
Frozen Heart: If no one else on your team can build this, and you have the gold, it's great against attack speed heavy teams.