I haven't played him a whole lot, but the runes/masteries setup I run was stolen from Meteos who plays him quite a bit at the challenger level.
Attack Speed Marks
Armor Seals
3 MR Glyphs
6 Flat CDR Glyphs
3 Movement Speed Quints
12 in Ferocity skilling: Fury, Feast, Vampirism, Oppressor
18 in Resolve skilling: Recovery, Tough Skin, Veteran Scars, Perseverance, Legendary Guardian, and Strengh of Ages
Alternations that I've made now and again are
HP Seals with 2 armor Quints, 1 HP quint, 6 Flat CDR glyphs, and 3 Scaling CDR Glyphs.
Then running Unyielding in place of Recovery, Explorer in place of Tough Skin, and Grasp of the Undying in place of Strengh of Ages.
Those changes felt better to me, it makes the clear a little bit harder, and you don't get that bonus chunk of HP to funnel into damage, but it feels like you swap a little bit of damage for more in fight sustain, and as Tahm Kench you should probably get off Grasp a few times in a good team fight.
The net result ends up being 98 flat health increase from the start of the game, easy to attain 10% CDR out of runes just for leveling up. The cost of this is being a little bit squishier and losing the bonus movement speed, which is pretty helpful to Tahm Kench. I'd try both sets and see what you think.
For items here's what I take. 
I build these every game if I can. Swifties are your new mobility boots, and the bonus constant movement speed is highly beneficial on Tahm, Deadman's movement speed is pretty much essential, and similar to Mundo, if you can find any excuse to build Spirit Visage, do it. As for the Jungle Item, you don't get a lot of use from Chilling smite, once you're in range to hit with your tongue, you can stick to them forever. Skirmishers prevents you from dying to invades, and often times turns around a fight to make that invader a free snack delivered right to your doorstep. You can opt for the Tracker's Knife if you'd like, but I feel the wards get out weighed by the utility Skirmisher's provides. Finally Cinderhulk is just a great item for Tahm, I see some people build Devourer, and if you're snowballing hard from the start go for it, but Cinderhulk is just a safer and more consistent choice in my opinion.
For items from there, ultimately I like to pick one of the two 20% CDR armor items be it 
If I'm looking for the damage I take Iceborn Gauntlet, if I need the extra tankiness I run Frozen Heart. Ultimately obtaining 
is a dream item for Tahm since his damage directly scales based on his HP, but this is where you can be really creative with your item choices depending on what's necessary. 
and if you're feeling really spicey you can look at 
or even an earlier 
so it can stack up.
The last three seem like really weird items, but Tahm does pretty well with magic penetration and has some pretty good AP ratios, meanwhile RoA gives him AP, HP, and more mana to run with. I usually don't run these items, but they have their situations. For example if we have a heavy magic damage comp, but nobody else has cause to build Abyssal, I'll pick it up, and it directly translates to more damage for our team, just for me standing in a teamfight, it also buffs all of Tahm's damage, as well as Cinderhulk and the gromp smite buff, which with Tahm you should be getting as it's pretty strong with the amount of HP he builds. If you have Thornmail and smite Gromp while having like 3k bonus HP, ADCs will actually kill themselves, it's hilarious.
Finally, as far as general tips, I like to start bot lane and try to get a really good leash to do the first camp smiteless, devour is comparable to smite in terms of damage, so getting a really good leash and devouring it can lead to a pretty easy first camp, to then translate into smiting the buff, as you can't devour it, and if you started with a leash on Krugs bot lane, you're aiming for Red as your second camp and it kicks your ass, so the HP from the smite is pretty beneficial.
Alternatively you could do the high xp focused clear where you skip your buffs run the small camps, back, come back through and do a full clear. This puts you very close to level 6 where your damage really turns on and your ganks become much more threatening. Until 6 it's not very easy to gank lanes, you waddle on in and typically the enemy team runs away, leaving you to only be able to successfully gank pushed up lanes, where other champions have much better gank tools. I personally feel that Tahm Kench belongs in a lane more than in the jungle he has very good gank follow up, but slightly below average gank initiation until 6 where you can just teleport in behind the lane, maybe with another lane stowed away in your belly.
