An important thing to mention is a Tahm Kench mechanic where you throw out Q and R at the same time with no delay by pressing Q at the exact time the ultimate runs out (and automatically throws the enemy out). Try it out in practice tool...

Account name: Spicy McFeast [EUW]
I went from gold to peaking master season 9 abusing Tahm Kench. Now trying the same thing with his new rework, which seems even stronger than season 9 Tahm Kench imo. I've tried different builds, but i am most confident with this kind of standard build.
I have 700k points on Tahm, which is far higher than the ammount of points on my other mains (at the moment i am a filthy OTP Tahm abuser, though)
Currently D1.

Anathema's Chains is very cost efficient, especially if they have a fed carry or you are going to duel an enemy champion a quite a lot. Getting an early lead and buying this item quick (after Bami's or mythic item) can allow you to snowball with ease.

Underrated items imo is Wits End (if ahead and vs a bit of magic damage), Knights Vow (if you have a carry that needs peel), and Turbo Chemtank (only if enemy champs have insane range and kite, and the team needs an engage).

Sterak's Gage could also be used.
I would stay away from Warmogs Armor, as Tahm's, E with a few points in it, is more than enough sustain - especially if you have a Spirit Visage.

Might add an actual guide with tips if the guide actually gets any attention...

Untill then you could watch this youtube vid which is quite helpful for learning Tahm top. It also has some very useful tips and tricks, so i highly reccommend watching it, if you're interested.(I did not make this video). Play Video (unknown embed type)