Flay can interrupt many gap closers, such as Jarvan IV's Demacian Standard + Dragon Strike combo or Shyvana's ultimate. I recommend watching for these initiations and attempting to use your Flay to counter them as much as possible.

Dark Passage can be blocked by enemies if they stand directly on it, or by enemies placing wards upon the lantern. I recommend throwing the lantern in front of your retreating ally's, rather than right on top of them, so they have room to click it.

After you hit a Death Sentence, you have a short amount of time before clicking it to throw Dark Passage to an ally. They can click it and ride along with you on the death sentence pull!

Thresh is very good against champions without good all in, since he is able to force fights with his E and Q. So champions like Sona, Blitzcrank who can’t win an all in fight with Thresh during the early game are all good matchups vs him. Against these champions he should be constantly trying to fight. Use Dark Passage on you and your teammate before going into to harass to ensure you win the trades. Pay attention to the map, and if you are worried about a gank stand behind your ADC with your shield ready.

For Ganks:
Throw shield behind yourself to get a teammate into the fray. Well they are in the air, Flash forwards, and immediately Flay the enemys backwards into you. Drop your ult, and well they are extremely slowed, throw Q directly at them for a guaranteed catch. If they still have flash up, be patient with your Death Sentence and wait until after they use Flash before using it.

Move around the map attempting to make plays. I recommend going to your strongest lanes and trying to snowball them. You should have Boots of Mobility by this time. I often will be constantly moving between mid and bot lane, attempting to shield my teammates away from ganks, or make plays on the lanes myself.

Make sure to keep the map warded with your Sightstone. It got buffed in the newest patch, and now you can keep 3 wards up at a time with just the normal sightstone.

This is extremely situational depending on what is happening in the game, but you should be looking to control the map and initiate plays upon the enemy team / keep your team alive.

Generally you should be sticking with your team.

1: Initiator: Use your Death Sentence or Flash to get into the middle of their team and drop your ult.
2: Peeler: Stay close to your ADC and use all of your skills to peel any enemies trying to get onto him. Do not stand directly on top of him, as you want him to be able to use your shield as a jump.