Here's how to get the card key in Saffron City:
1. Talk to the man in the Game Corner. He's standing in the center of the room with a bunch of slot machines. He'll offer to give you the key if you get 50 coins.
2. Earn coins at the Game Corner. There are various games to play, and the best way to earn coins is by playing the Voltorb Flip game.
3. Collect 50 coins. This can take a while, but it's the only way to get the card key.
4. Return to the man. Once you have 50 coins, go back to the man who offered you the deal, and he will give you the card key.
The card key is needed to access the Silph Co. building, where you'll find the legendary Pokémon, Mewtwo.
Good luck!