Flash- There is nothing better you can take, flash is flash, and on thresh you can pull of some tricks with it.
Ignite- Thresh has a lot of kill pressure, and being agressive is a best way to plaz him, ignite helps out a lot in ending that agression with a kill.
Exhaust- It is also a good option if you dont want to take ignite.

Start: - Ancient Coin and Relic Shield are 2 best options for Thresh as a support, take your pick- Relic shield will give you more sustain (for your teamm8 as well), and coin will give you some mana reffiling. You should usualy also start with 3 Health Potions, but if enemy bot-lane isnt so agressive, you can go for a Refillable Potion (though I usualy don't).

First back: Standard for a support, upgrade your supp item, take Boots and a Control Ward, and when your supp item upgrades from it's passive quest, take a sweeper lens.

Boot upgrade- If your lane is winning, take Mobility Boots, it will help you get back to the lane, and also they will help you roam, going to help your mid-lanner from time to time isn't a bad idea. If your lane is losing take defensive boots ( Ninja Tabi against haevy ad comp, and Mercury's Treads against haevy ap comp, but if your bot-lane oponents (not counting if you have a terrible adc ;) ), are both ad take tabis, and if they are both ap take treads.

Core- Items listed here are Frozen Heart, Gargoyle Stoneplate and Locket of the Iron Solari. Frozen hearth is great because of that huge number of armour that it gives, cdr and mana are also really great on thresh, and it's passive is great. Stoneplate is great on thresh because it gives both mr an armour, about its passive, it req. 3 or more enemys to be near, so in lane thats your 2 oponents and their jungler, and than it gives a LOT of protection. It's active is also great on thresh, couse think about it- in a lot of team fights you will engage first with your Q, and you will go in, so you found yourself in a lot of enemies, stoneplate's active than will give you a LOT of hp, so you will hit your cc for sure, and probably survive a long time, enough for your soloQ team to react. Locket, again gives both mr and armour, and its active shield can absorb a LOT of dmg. For purchase order, you want to take 1 core item, than 1 tanky item, and you do that until your inventory is full. And yeah, and part of your core are your upgraded supp items (you will ofcourse take 1), that is really important to have for the vision it provides, so you should upgrade your supp item first, than take another core item, than do the order I told you (1 core item, 1 tanky item,...).

Tanky items: These are tank items that I think are the best items for Thresh. I'll go over them quickly. Abyssal Mask- Take it when you need mr, and your lane buddy deals magic dmg (someone like Swain, Corki, etc..). Thornmail- Take it when enemy team has at least 2 mostly aa champions, really nice passives, nice stats. Randuin's Omen- take this when there are at least 2 enemy champions that do crits in a game, or if you are facing a Yasuo in lane (if that's the case, your purchase order should be this: Fully upgrade your supp item-->Frozen heart-->randuin's). Ohmwrecker- this item you wont see a lot, take it early if you are stomping your lane so you could dive more easily, and you will probably sell it in the end game to get a space for something else. Warmog's Armor- take it if you feel that you need that regen.

Elixir- When you are full build you want to take Elixir of Iron-why wouldnt you take an elixir? And This 1 is the best of the 3 for this build.

Control Wards-Always have 1 placed!

You should start with E( Flay) as it gives most dmg lvl1, and is simply strongest ability in lane. Than go for Q( Death Sentence) and than take W. Don't put your first point when you spawn, first see if you will be envading with your jungler, if so, start with Q, but that will make you little weaker in lane at lvl1. I like to put another point into E at lvl4 as it is the strongest ability in lane, than I go for an Q max as it is the strongest ability later on. After Q, max E, and finish off With a W max. Ofcourse you put a point in your ultimate whenever you can.

Q- that's your kill set-up tool, displacement tool, engage tool, your only scource of "mobility". When wanting to engage (planing to use your second part of the q), try to aim in a way that if you mid your original (champion) targed, you will still hit a minion near them, so you can dash to a minion and get closer to them in that way.
W- this helps your carry follow you, its easiest save tool, and it is also a trick tool (you can throw it into a river/tri bush while being chased so that your oponent thinks that your jungler is here, they usualy back off - bonus effect of doing this is that when your jungler really comes, they might not back off when they see the lamp. I wouldn't advise you to use it as a shield, as shilding of this ability isn't that good, but if you or your carry are dying to ignite, it's worth a try)
E- (active effect)engage and disengage tool, displacement tool, (passive effect) and also helps you poke in the laning faze- don't aa the wave if your 2 oponents aren't hard pushing, try to fully "charge" you E's passive, and than auto 1 of the oponents (it doesnt have to be a carry, poking a supp is also completely fine, don't risk minion aggro, and unnecessary return dmg).
R- helps you lock oponents down, and can help you escape.
-Dont forget that your abilities will do fine dmg early on.
-Your full engage combo is this: Q --> W (on your carry) --> Q(dash part) --> R --> E

Aftershock- really great rune, helps you survive longer when you hook into somebody, and will add a bit of dmg to your dmg output.

Bone Plating- helps a bit around poke, and (especily early) if it is up, it will help you out-trade your oponents when you q to them.

Chrysalis- I like that 50hp at the strat, about other part of the rune i don't care.

Unflinching- that tenacity and slow resistance does help out.

Cosmic Insight- free cdr, it isn't much but it is something. If you like some other rune, feel free to change out this one.

Biscuit Delivery- gives you sustain and refills some of your mana, simply great.

Well, as with other supports, you want to help your adc get fed (or batter say bot-laner at this point) and protect him/her. With thresh you are your teams play-maker, force aggressive plays from the start to the end. If enemy bot lane is stronger than yours at the start of the game, you don't need to take your q dash, you can just open a big space for your adc to poke your victim for some free dmg, when you feel the time is right, go for the kill, get your carry fed, force dragons and early towers. Remember, first turret gives a lot of gold, and drakes are drakes- thats the way you carry the start of the game- force those kills, after which force those objectives. In mid game, if you won your lane, try to roam, and win mid lane as well, and if you get enemy mid laner to go back or you kill them, force mid turret, and than rush back to your carry so he/she wouldn't die, and throw the advantage you worked hard to get-thats how you carry in mid game (if you didn't won your lane, just stay bot, and make sure your carry doesn't feed anymore, and keep in mind that not everything is his/her fault). In late game, you again need to force even more plays, so if you are ahead, force good team fights, and forcing objectives is a must later on, at all points you can lose everything, that's why you need to end the game as soon as you can. If you are behind though, you should try to get pick-offs, yeah with a full supp build you cant really 1v1 anyone (besides their support), but bring somebody with you; even if you are behind, you can win fights with numbers, and after winning a lats say, 4v2, go for a tower/drake, do this once and you just started catching the game that they started throwing, do this multiple times, and you won't be behind anymore.

Thresh has apsurde amount of cc, great peel, and nice kill set-up, he is really fun to play and I hope this guide helped you! :)