Ah, right.
I'm not exactly sure what mode you are trying to play (since I haven't played Pokémon Stadium that much), but it seems that the game expects you to insert a Transfer Pak (only usable via the N-Rage Input plugin) with a Gameboy Pokémon game and an accompanying save file from the same game attached to the Transfer Pak.
I'd really like to hear some input from people who have played Pokémon Stadium more than I have.