Blastoise - After beating Lt. Surge, go to the middle of Vermillion City. Officer Jenny will be there, and she claims that Squirtle had been getting into mischief. This is a reference to the episode "The Squirtle Squad" where a group of Squirtle have been getting into mischief.
Charizard - Charmander can be found above the Nugget Bridge; at the north-west corner of Route 25. There will be a trainer there, and claiming that he is a bad trainer, he'll offer you Charmander. This is a reference to the episode "Charmander the Stray Pokémon", where a trainer called Damien abandons it in the rain.
Venusaur - Bulbasaur can be found to the house West of the Cerulean City Gym, where a lady offers you a Bulbasaur that she nursed back to health. (NOTICE: You can ONLY get Bulbasaur if your Pikachu's happiness is high enough.) This is a reference to the episode "Bulbasaur and the Hidden Village", where a girl called Melanie takes care of injured Pokémon in the middle of a forest, with Bulbasaur being the guardian (wouldn't be too hard to get past, eh? :P).
Pikachu - I haven't found out yet *sarcasm*
Snorlax - In front of Diglett cave, there is a Snorlax blocking the cave entrance. Go to Lavender Town and you can get a Poké flute in the Pokémon tower. Use it on the Snorlax and it will wake up (gl catching it, it's got a capture rate of 25!)
Lapras - After defeating Gary in Silph. Co (in Saffron City, I believe), to the left, there's a bro that gives you a free Lapras! W00t pl0x!
And... That's his team. Hope I helped :D