Tahm Kench is a tanky, high damage champion. His passive allows it so that it makes it hard for the enemy to come close or even farm. Farm freely and when the enemy is getting brave enough, start autoing them. If the enemy gets three stacks of Tahm's passive, then go aggressive. Start by landing a Q on them to stun them in place. Auto a bit after they are stunned and, just before the stun is over, use your W to eat them, then spit them in the opposite way of their turret. Even if the enemy is passive, use your W to eat a minion to shoot at the enemy. If it lands, a does a good amount of damage as well as apply a stack of Tahm's passive.

Team fighting as Tahm is tricky. Tahm's abilities make it so that he can only attack one person aside from his E, but that only works if a minion is consumed. When in team fights, it is best to just keep the enemy off of your carry. Do this by either: eating the carry if they are being focused, targeting the enemy carry with your passive, or acting as bait for the enemy by using your E to gain a shield of the health loss, making their attempts useless and easier to cleanup for your team.