Tahm Kench's kit has no AOE camp clear, and is rather slow. Always start blueside and take gromp, wolves and then your red, before pathing to scuttle or a gank. Never gank without W, unless an enemy is very pushed in. Rush early Tiamat and Bamis for camp clear.

Once you have completed your mythic and gotten boots and Tiamat, you become much more capable of dueling and gaining objective control. Feel free to play more aggressive, Tahm has decent dueling and his kit allows easy escapes with his shield and slow, to allow you to escape from fights you can't win. Before 11 your ult doesn't do much in terms of ganking, as its range is too short. You can try to use it to sneak into a bush and ambush someone, or steal an objective.

Lategame Tahm is a nightmare to play against. Hes a stack stick that becomes incredibly tanky, with a passive that allows him to deal out considerable damage. Use your ult to give your team mobility, and in team fighting peel for your carries. It is much more recommend to use your W on your own team here- eating them and spitting them out somewhere safe is essentially a flash + zhonyas.

When ganking try to set up with a Q to slow - if you can't hit it your chances of reaching someone and getting your 3 autos off for a W are abysmal, and once you can get your W off and carry them away from their tower to put them out of position and between a rock and a hard place, where you and your laner should be able to finish them off.