Thresh is an extremely versatile champion. Each ability of his can be used to engage as well as peel. With his Q (Death Sentence) don't expect to hit it like you hit other skill-shots (using mechanics I mean, like Blitz hook or Ez mystic shot); you land it using mind games because of its wind-up. You have to get people in an area where they can't escape, predict where they will dodge to, etc. His E (Flay) is probably his single best ability IMO. It's more difficult to use than you would think so you may want to smart cast it at first. Also be aware that it will cancel dashes, so make sure to save it for things like Tristana jump and Lucian dash. His W (Lantern) can be used in many unique ways. You typically think of it as an escape for another, but you can also use it to bring people to the fights. It's also a good mind game tool. Don't be afraid to throw it back like you're bringing your jungler when they're not there and walking towards your opponents to zone them. Also, do not underestimate the shield it gives. His ult is pretty self explanatory lol.
Thresh also has some pretty good damage which shouldn't be forgotten about. Make sure you're harassing when you can with him. Depending on your lane match-up you can be aggressive or passive and be effective at both. For example, if you are laning with a Jhin, you have insane kill potential level 2. In this lane, Flash + Ignite is a very good option. When you hit level 2, don't be afraid to Flash + Flay + Ignite + Death Sentence. You can chain all this with Jhin's W, and if it's executed properly, will AT LEAST get you a flash on the other side. Be sure to also practice pulling people to enemies. This is done by hooking someone, throwing back the lantern, and pulling them with you for an engage. This can be amazing depending on who you have on your team (delivering a Skarner to someone so he can deliver them to your team is sooooo satisfying).
Thresh, IMO, is a carry type support. If you play the game well enough, you can absolutely carry your team with your utility. He can single-handedly win team fights if you make the right plays. He is definitely difficult to pick up and master, but when you put enough time into him to get at least decent, my goodness is it rewarding.
Good luck my friend :)