You need a champ with some sort of AoE damage and at least one skill for peeling.
AoE basic abilities allow Jhin to proc his W root more effectively. Good examples of this are Morgana, Zyra, Soraka, Brand, Vel'Koz, Fiddlesticks, and Lux.
Peel abilities are pretty obvious. All champs listed above have some sort of peel, but the better examples are Morgana and Zyra, as their peel/zone is a bit more reliable. Also, in this department, champions like Leona, Taric, Thresh, and Braum work very well. They can even allow Jhin to follow-up initiation with a stun/slow/hook into a Jhin root.
Laning: try to setup poke for his W proc. Zone the enemy laners into bad pathing patterns so as to make Jhin's W easier to hit. Also try to use Jhin's traps to zone the enemy laners into choosing either to hit his traps or take your harass. When Jhin ults, you have to make a snap decision: locate the jungler on the map. If you can't see him, stick closer to Jhin as his ult locks him into place. If you can see the jungler, assess how quickly he can react. If their jungler is far away, push up on the targets Jhin is aiming at, trying to hit them with any sort of CC you possibly can.
Teamfighting: look for picks. Try to layer some sort of damage onto enemy champs that are out of position and/or squishy so Jhin can possibly hit a W root on them. Try to stick close enough to Jhin that you can respond to a dive effectively. If you're playing a tank support, save your best peel for when Jhin is getting dove. A good rule of thumb is to be in range for Knight's Vow to transfer damage onto you (if playing a tank support). Or you should play close enough where you could cast a shield or pop Locket on Jhin to give you time to close the gap. When Jhin ults, it's the same as before, except your job as support is to stay close to Jhin to peel anyone that sneaks through your front line to kill him. The exception to this is if you're cleaning up the fight - then you should just push onto the enemy to pressure their escape.
Itemization: do not build Ardent, even if you're playing an Ardent support, unless it helps another member of your team (i.e. Kindred, mid Corki, Master Yi, etc). Jhin doesn't scale well enough from the attack speed buff to make the Ardent a good buy if Jhin is the sole auto-attacker on the team. You're better off getting Locket and Redemption, as keeping Jhin alive through his reload and during his ult channel is far more important.
Your main objective is to keep his immobile ass alive. Sure, recently Hail of Blades and Stormrazor have made Jhin a beast, but these tips were relevant before these issues, and will be relevant after these issues. There are more finer touches to support, but those touches are pretty universal to support as a role, and aren't really Jhin-specific.
Hope that helps.