Well the short answer is he is like a mix between blitzcrank and amumu.
The better answer is that if you play him as a support to bot lane you will be able to grab(which also interrupts the enemy) and pull the in (very effective for low health enemies under their tower as well as tower divers taking a big risk). The rest of his abilities are also for disrupting the enemy. His DARK PASSAGE is able to save any blind carries that get ganked as well as gives everyone int the area a shield(this is both defensive and offensive, making tower diving easier and making harassing and attack strait up less of a gamble). Lastly a not so well known attribute of DARK PASSAGE is that if you throw it in the area of a soul it will consume it meaning it is very usefull in lane if the soul is out of reach or you dont want to chance it FLAY is very effective in close range for stopping enemies in their traps and putting them back a few steps. This is also a offensive(stop them from running away and giving your carry at least 2 more shots on them) and a defensive(throwing away and deterring chasing enemies) ability. ALSO this ability interrupts anything from a caitlyn sniping to a Nunu charging his ult (I have not fought every champ with him but everyone i have so far i managed to interrupt). THE BOX is Thresh's ultimate it brings up a pentagonal wall around thresh(like amumus ult it cannot be aimed and is centered around Thresh himself). This is best used to start a team fight or right after it starts. The best tactic is to grab someone with DEATH SENTENCE and the pull yourself towards them and activate the box (much like the amumu bandage toss into ult combo). The box slows enemies for 99% of their movement speed wich might as well be nothing.

The best thing is to play safe. place the ward once you start farming the lane and either hide or keep moving behind the caster minions. As a support you don't really need farm so let the carry take everything but do your best to get the souls, use DARK PASSAGE if you have to and can spare the mana. Early game before you have a chalice of harmony try to keep ability use to a minimum, use only when your are almost sure that u will achieve what you want otherwise you will end up having to go back before you have enough money. Lastly try and dodge enemies attacks, it sounds obvious but you are not yet a tank and you will take quite a bit of damage. The most important part is to coordinate with your jungler and carry. You should be the one starting a gank by grabbing a champ with death sentence dragging them closer (he pulls them twice, COUNT!) and right before the end you should jump to them and immediately through dark passage and flay in quick succession so stop them from running away. Also try throwing death sentence into the bushes if you know enemies are there they will probably not be expecting their surprise attack to be turned around by you grabbing one and jumping toward them with your carry shooting them from afar.

By this time i hope you have atleast a few assists and have the build upto or past chalice of harmony. I suggest keeping your eye on the minimap and to help towers and allies close to you if possible otherwise just keep in lane till the enemy tower goes down. And remember you are support(a hell of a support but still :P ). stay with allies and make sure you participate in teamfights if you are evenly matched(if they outnumber you or for watever reason you need to retreat through Dark passage near your allies so that they can use it to go to you if need be).

This totally depends on your allies. if they have been good the whole game through you should have quite a few assists and have a big part of the build already. If you do you can start to use your ult more frequently because you should have a lot of CDR. its teamfights al the way for you now, in between try and jungle or farm lanes for more souls but support your team fully. by now your are quit tanky so you should be able to be more on the front lines(but still behind the full or bigger tanks). there isn't much to say about late game with tactics in mind it all depends on the game so far, are they fed? are you fed? is your team full of team players? are they trolls? so that is the risk you take by being support.

this was my first guide and i don't really know if it will help but i thought i should to one because so far the previous builds on this site hasn't really helped me, so if you like nothing of this guide please just try the build and tell me what you found when you used it :)
if you have suggestions what i should change on this post feel free to tell me and also if you would like other builds (though i don't think i have a self made build for any other champ but darius).