Since you're playing a unique champion that's not as well suited for the jungle compared to others (like Ivern) you have to be a bit war as you may be executed a few times before you get the hang of it.

Since Tahm Kench is very mana dependent early game you want to start at the Blue Sentinel (hopefully your allies will be kind enough to leash you) and then you make your way to Gromp, Wolves then over to the Red Brambleback, from there you can roam and do your own thing really, but I advise you try to hit level 3 before doing anything too risky (which this route should easily allow you to).

When you get 6, the world really is your oyster, just do whatever you feel like at that point, keeping a close eye on the map for when you can pounce an unsuspecting lane, show them why they call you king!.

Tahm Kench is a really underrated character and has so many tools to make ganks and push them in his favour that I'm surprised that nobody really does this. It is more of a fun build though and nothing you should jump into ranked with. Just have fun!