Hi, my name is Guy, i've been playing League since patch 5.4 and i've been maining Thresh for A LOT of time, so i'm writing this guide to share my experience.
Thresh is most likely the hardest support to play, since he is also the most versatile, and can be played both passivly and aggressivly.
All of his abilities have a very unique pattern to them, so he's a bit different from all the other supports you may have played. BTW, there is a way to play him as an ADCarry, but i really don't reccomend it, as there are other ADCs that are a lot better than him (currently Lucian and Ezreal are monsters, followed by Caitlyn and Sivir).
Because of his versatility, Thresh doesn't neccesarily care about the meta as he is almost always a viable pick, and in the hands of the perfect player, Thresh is the easiest pick to carry with as a support.

What?! already confused?! well, supports can utilize both Exhaust (as a defensive maneuver or easier chasing) and Ignite (higher kill pressure and vision on Twitch {F*ck Twitch}) and Thresh is no different. You take Ignite on the aggressive match-up and Exhaust on passive one.

Pros:

-The most versatile support in game
-Combines high kill potential in lane with massive defensive utility
-Strong in any kind of meta/botlane due to his versatility
-Has a very high skill cap

Cons:

-Lacks sustain (and the Relic Shield nerfs don't help...)
-Takes time to practice and use Relic Shield
-Very high skill cap ;)
-Good utilization of his skillset may require a certain level of teamwork

Greater Mark of Attack Damage

We pick these because last hitting for the use of Relic Shield's passive is really hard for Thresh since he is ranged. These should make it easier, although you should remember to use Flay's passive for easier last hit. If you get REALLY good at this, i suggest switching to Greater Mark of Armor, since you benefit from defensive stats early.

Greater Seal of Health

simple, Thresh's sustain is very low early, these come in handy for that purpose. Always remember: never use the same seals and quintessences, since you want some of both stats.

Greater Glyph of Scaling Cooldown Reduction and Greater Glyph of Cooldown Reduction

since Riot decided to remove all 5% CDR bonuses, it is simply not worth to go all flat or all scale CDR runes. So, we take 6 flat CDR for 0.83% each (giving total of 5%) and 3 scaling CDR that give 0.09% per lvl each (so at lvl 18 we get 5%), so we end up with 10% CDR.
But what about the magic resist? good question young student. Since the monsters that used to rule botlane called Corki and Mordekaiser are no longer a monsters, you benefit more from CDR than MR. BUT!! if you are laning vs. an aggresive a poke ap support such as Morgana or Sona, it's definitely worth to switch these for Greater Glyph of Magic Resist. This is all according to current meta picks, and even if you don't take the MR, you still have the extra hp from your seals.

Greater Quintessence of Armor

Thresh has a serious sustain problem in the early game, so the armor is a really nice help.

Thresh uses two mastery pages, since picking one mastery page in the wrong match-up can be fatal.
As i already explained, Thresh can be picked into both aggressive and passive match-ups. But, using the page above in an aggressive match-up is a waste of resources. Instead, this page fits much more, and lets you do those shenanigans you wanna do in your bot.And for reference, here again is the passive match-up mastery page.

Using Wanderer is obvious for every support, since your job is not only help the ADCarry, but help ALL your team. now, helping to top lane is a bit far, but roaming to mid lane with those Mobility Boots and some extra movement speed is really nice and can snowball a lane really hard.
Secret Stash , Meditation , Recovery and Veteran's Scars help with Thresh's sustain in the early game.
Choosing between Explorer and Tough Skin is a bit hard, but the rule of thumb is this: if your play style/match-up give you a lot of opportunities for roaming mid, you should pick Explorer . If not, then pick Tough Skin , as it does help you in lane.
Bandit is a nice source of money, you may not notice it, but it actually gives you quite a lot of money.
Insight is important because it allows us to use Flash more freely, so Flash Death Sentence are more available for the skilled Thresh player.
Now, the big choice!!! Do i pick the Intelligence and Thunderlord's Decree for EASY early trades with AA-> Flay->AA on lvl 1, OR do i pick the Swiftness and Bond of Stone for the damage reduction and tenacity (=less time effected from CC)?
That's a question of preference, match-up, and play style. I won't say which one is better for each match-up, but i will say that i personally like to play the aggressive page A LOT more.

Passive: Damnation
Thresh does not gain armor per level. Instead, Thresh collects the souls of dead enemies by approaching them or by placing Dark Passage's lantern nearby. Souls permanently grant 0.75 armor and ability power. Champions and large minions always drop a harvest-able soul. Small minions only sometimes drop a soul. A soul will only drop if the enemy unit dies within 1900 range of Thresh. Souls are visible to allies, and only become visible to enemies if the enemy team has vision of Thresh. Souls disappear if not picked up after 8 seconds.
TL;DR:get those souls, get free 0.75 Armor and AP for each soul= Free buffs. Secret Easter Egg: if you ever reach 255 souls (won't probably happen, but...:^)), The number will reset to 1 once you get the 256th one, but the bonus won't. The limit for souls is 999,999 souls, so its pretty much infinite in a game. BTW, when killing Nunu & Willump, he drops 2 souls instead of one, so that's nice.

Q: Death Sentence
Cooldown: 20 / 18 / 16 / 14 / 12 Cost: 80 Range: 1075
Thresh throws his scythe, dealing 80/120/160/200/240 (+50% of ability power) magic damage to the first unit hit and dragging them towards him for 1.5 seconds.
Additionally, he may reactivate the ability to leap to his chained enemy.
If Thresh hits a target, Death Sentence's cooldown is reduced by 3 seconds.

This is Thresh's bread and butter, EVERY good Thresh must know how hit hooks, predict movement and all movement abilities such as Ezreal's Arcane Shift, Katarina's Shunpo and Lucian's Relentless Persuit, and as an addition to all that, predicting an invisble hook vs. Rengar's Thrill of the Hunt or Shaco's Decieve is also possible.
In the aggressive match-up, you max this second after your The Box, and in the passive one you max this third after Flay and The Box.
W: Dark Passage
Thresh throws out a lantern that shields the first ally from damage for 60/90/120/150/180 (+40% of ability power) for 6 seconds. The first ally to click the lantern with be pulled to Thresh. Allies can only receive the shield once per cast.
The lantern collects nearby souls while out.

This ability is SO ****ING GOOD when used correctly. You can use it to both engage and disengage, peel for your ADCarry with a nice shield or even grab a distant soul. PUT TO NOTE!!! no one can take the lantern if an enemy champion is stepping on the lantern, so position it carefully.
On both match-ups, you max this fourth since its scaling isn't really that effective and the other abilities get A LOT stronger maxed than this one.
E: Flay
Cooldown: 9 Cost: 60 / 65 / 70 / 75 / 80 Range: 500
Active: Thresh sweeps his chain in a line, dealing 65/95/125/155/185 (+40% of ability power) magic damage to all enemies hit and pushing them in the direction of the swing. Enemies are then slowed by 20/25/30/35/40% for 1 second.

Passive: Thresh deals bonus magic damage on each auto attack. The damage is equal to the number of souls he has collected plus 80/110/140/170/200% of attack damage, based on length of time since last attack.

Now this skill is one of, if not the biggest difference between a good Thresh player and a bad one. Using this correctly means (1)knowing when to use,(2)knowing to Flay forward or backward (push or pull), (3)timing it correctly as it can stop dash movements, such as Lee Sin's Resonating Strike (second Q), Leona's Zenith Blade (E), and Tristana's Rocket Jump (W), (4)Utilizing the passive in the laning phase to deal a **** ton of damage.

In the aggressive match-up, you max this third after Death Sentence and The Box, while in the passive one, you max this second after The Box.
R: The Box
Cooldown: 150 / 140 / 130 Cost: 100 Range: 450
Creates a prison of walls around Thresh, dealing 250/400/550 (+100% AP) magic damage and slows any champion that collides with a wall by 99% for 2 seconds.
Once a champion collides with a wall, the wall is destroyed.
Any other walls struck by any other enemy champion slow for half the duration.

Is this **** real?! 99% slow for 2 seconds and that much damage?! YES. Use with caution, can be deadly. STORY TIME!!!! I actually once had a QUADRA KILL just from the enemy team being low and stepping on the box, soooooooooooo.... (hint hint, don't accidentally KS your ADCarry with this TOO MUCH :^))

You max this first, as every other ultimate skill.

starting items:

you always want to pick up the Relic Shield and 3 Health Potions as they let you survive in lane. Although Last Hitting with Thresh is a *****, it's still a lot better than the Ancient Coin.

early game:

First and foremost, Sightstone. DO NOT UNDERESTIMATE THE POWER OF WARDS. After this, you wanna pick up Mobility Boots or Ionian Boots of Lucidity, depending on whether you want to roam a lot or not. Don't forget to switch your Stealth Ward for Sweeping Lens as you already get wards from your Sightstone.
you almost always want to pick up the Eye of the Equinox, unless the enemy team is full of assassins, then you wanna pick up that Face of the Mountain to keep your ADCarry safe with a nice extra shield.
Then, even if the enemy team has only one magic damage dealer, you always want to pick up Locket of the Iron Solari as your third item, as it provides magic resistance for everyone and a nice AOE shield that scales with level. I wouldn't reccomend taking Banner of Command on Thresh as the tanky stats and CDR benefit him more than the AP, but if you really want to, that's your choice.

mid/late game

After building the core items, we have a few options to choose from, which i will now go over: purple=excellent pick,blue=very good pick, green= okay pick,yellow=situational pick/meh pick,red=bad pick
- Dead Man's Plate- Gives a **** ton of tanky stats, plus the passive that gives movement speed is really nice. My play style involves a lot of roaming to mid lane, so this item is almost always my fourth item.
- Frozen Heart- Gives a lot of armor which is nice, but the real thing about this item is the 20% CDR which is AMAZING on Thresh, and the mana is nice too. I would pick this item Vs. ADCarries/Team that utilize Attack speed a lot such as, Aatrox, Ashe, Caitlyn, Draven, Irelia, Jax, Jinx, Kalista, Kayle, Kindred, Kog'Maw, Master Yi, Nocturne, Shyvana, Sivir, Teemo, Tristana, Trundle, Tryndamere, Twitch, Udyr, Vayne, Vi, Volibear, Warwick, Xin Zhao and Yasuo.
- Randuin's Omen-A nice add to the collection: armor and hp benefit you nicely, the damage reduction from crits is really nice Vs.: Ashe, Corki, Draven, Gangplank, Graves, Jhin, Jinx, Kalista, Kayle, Kindred, Kog'Maw, Lucian, Master Yi, Miss Fortune, Pantheon, Quinn, Rengar, Shaco, Sivir, Teemo's new on hit build, Tristana, Tryndamere, Twitch, Varus, Vayne and Yasuo.
- Turbo Chemtank-An ok item, you benefit from it's hp and mana, and the active is good for a team comp with a lack of initiation, so this is a situational pick.
- Warmog's Armor-Since riot decided to add 10% CDR to this item, it is actually not sh*t anymore. The hp is nice and all, but there are better items.
- Banshee's Veil- If you need some more magic resist, this should be your pick. The passive spell shield is nice as well.
- Spirit Visage-Less good than Banshee's Veil, but if you buy a Warmog's Armor and you got some cloud drakes, then this is a nice pick. The CDR is nice and all, but there are better sources to get it.
- Zzrot's Portal-If your team comp is a split push based one, then this is a nice pick up, but you should have more than one in your team. If not, then this isn't really good.
- Ruby Sightstone-If you chose to upgrade your Targon's Brace into Face of the Mountain, then this is a nice pick to upgrade your Sightstone, but i would do it later into the game, after i finished my Locket of the Iron Locket.
- Mikael's Blessing-This item is REALLY good for keeping your ADCarry alive, the heal is nice and the active is AMAZING, plus the extra magic resist and CDR that really don't hurt you.
- Thornmail-Meh, this isn't really good unless the enemy team is a full AD comp. The armor is nice, but the anti-on-hit-users passive is weak.
- Guardian Angel-********it, your'e the devil, not an angel. But seriously, this item doesn't fit in your build, because if you died you probably suck(xD)/lost anyway, this item isn't gonna save you.
- Ohmwrecker-Are you trying to troll me?
- Iceborn Gauntlet- Thresh is a tank, and this is actually a very offensive item. Doesn't fit in your build.
- Sterax's Gage-Same reason, too offensive and bruiser-intended.
- Abbysal Scepter-Let your midlaner build this one, there are better magic resist items for you.
- Elixir of Iron-After full build, this is a really nice addition to get you really tanky.

Laning phase

- Thresh has absolutely no sustain in his kit up to lvl 3 when he gets a nice shield from his W, and you have to manage with your relic shield, BUT!!! the damage and CC Thresh can output is absolutely amazing, and his goal in the laning phase is to win trades and poke the enemy ADCarry with long range AA while trying to deny him CS with hook pressure.
Try to back when you have 800g-1500g or you'll stay behind in lane. When you back, sightstone is obvious, a pink ward is nice, boots of speed are wonderful and if you have extra 200 gold, pick up that Rejuvenation bead for your Targon's Brace and a pot for sustain. Don't forget to switch to Sweeping Lens once you have Sightstone and an Oracle Aletration once you hit lvl 9.
Your "combo" in the laning phase is always Q->Flay backwards->AA->AA, and add that Ignite if you can ensure that is indeed a kill. It's fine if you take a kill or two in the laning phase, as long as it's KS for Kill Secure and NOT for Kill Steal. Your ADCarry will always deal more damage than you and you have to respect that, But that doesn't mean he can treat you like a slave.
In lane, position your self aggressivly at the side of the enemies' minions, so using Death Sentence to deter and not only hook is possible, so you can deny XP and CS from enemy laners.

Mid Game

- Here you fall off a bit, people start to buy their defensive items and you don't scale too much with base stats only. That's the point when you should probably start going mid and initiate a team fight.
Play Video
That's what a bad Thresh does. You can do better. You go ward the enemy jungle, you buy a Locket of the Iron Solari, that gets you a **** ton of value AOE shield that scales with level + FREE MR FOR EVERYONE. You buy a pink ward and an Oracle Aletration and clean enemy wards, and most importantly, you try and get a pick kill before the fight starts, so you can actually 4v5.
Remember, if you got ahead from your lane, it doesn't necessarily mean that all other lanes did too. Try and look how is your team doing, and itemize accordingly. For example: you did well in lane and your Miss Fortune is now 3/0, but your Syndra has died to their Diana 3 times. First of all, was that your fault? No. Could you have helped Syndra so that she won't die so much and maybe get a kill? Maybe. Do you want to pick up a banshee's veil after your locket against a fed Diana? Of course.

1)"That was faster than expected": One trick not a lot of people don't know about Thresh's Q is that you can reduce it's cast time by 0.5 seconds by canceling it's animation by using Flay first. This is a VERY useful tip in higher ELO's because it ****s-up the target's sense of prediction, so it's harder for them to know when it's gonna hit.

2)"Mind F*ck gank": You can do this sometimes in lane when you know river is not warded, and throw a lantern to the river so the enemy botlaners think this is a gank, when your'e actually just scaring them and denying them CS and XP. In higher ELO, this is harder to excecute because people look at the map and have better jungler awareness, so if your jungler just ganked top, don't expect this to work.

3)"All aboard the Thresh Express": to use this, you probably have to count on your ally to time this well, or maybe you're premade, so inform him that your'e gonna use this. place your W, then move to max range, hit a hook then jump to target on second cast of Q. while you do, your ally should take the lantern. Result: you and your ally just did a distance of almost tower to tower in mid lane in less than 1.5 second, and you both reached your target on time. DO NOT, however, use this recklesly, as it can lead to a lot of funny fails, and cause some embarrasing tower dives.

4)"super thresh": i won't explain this one. just watch and laugh to your heart's content: Play Video
put to note, at the start of the video you can see the correct use of the Thresh Express.

5)"The LVL 2 All-In"- you should almost always use this in the aggressive match-ups, consider using on the passive ones, as it can be a bit harder without the ignite.
On level one, you push the wave as hard as you can, if you need to, even tell your ADCarry to help you push the first wave very hard. Objective: reach level 2 before the enemy laners do. You'll hit level 2 on the third minion on the second wave, so time this well. Once you reach level 2, you initiate a fight with Q/E/Flash+E to CC chain the enemy ADCarry (specifically on Soraka lanes you want to target Soraka more than the ADCarry) and get a free kill, probably first blood. Reminder: even if you just get a flash from their ADCarry, that's fine too, because now you have 5 minutes that the ADCarry doesn't have a Flash. WHY THE HECK DOES WORK SO WELL?! because Thresh has a REALLY big power spike on lvl 2, since both Q and E + 2AA+ Ignite deal (Approx.) 350 damage BY YOURSELF, while the avarage level 1 ADCarry has 600 hp, so that's really strong, although it is relient on you hitting your skill shots.

I know i'm not the best Thresh main and there are a lot of better players than me. So here is a list of players/streamers that you should watch:
-Rayskat- https://www.youtube.com/user/reimond30
-I only Hook- https://www.youtube.com/channel/UCyOSssNmZu4Bq0U435WfT9A
-CPTAnton-https://www.youtube.com/channel/UCE3-iS8XT2fAlQClWm79tDw
-LastShadow8's Coaching-https://www.youtube.com/playlist?list=PL3B5Xqi5fDG8NLeSLWBnaThW3ijk_CtDb
-Krepo's stream- https://www.twitch.tv/krepo
-Aphromoo's stream- https://www.twitch.tv/aphromoo
And i would like to especially reccomend you watching some of rayskat's videos as they show very nice examples of some of the tips and tricks i've listed here.
I hope you enjoyed reading as much as I enjoyed writing and thank you for reading this far. Please rate and comment if you liked the guide :)