When you start the game, you have a choice to start out with one of three Pokémon: Bulbasaur, Charmander, and Squirtle. Squirtle, a water Pokémon, does the best against some of your earlier enemies. If you choose Charmander, a fire Pokémon, you'll have to work a lot harder in the earlier parts of the game. Bulbasaur, a grass Pokémon, is somewhere in the middle.

After you choose your Pokémon, your rival (who will from now on be conveniently referred to as Gary) will choose the Pokémon that is strongest against the one you chose.
For example, since water is stronger than fire, if you choose Charmander, Gary will pick Squirtle. If you choose Bulbasaur (which is weak against fire-type Pokémon) Gary will take Charmander. So, right from the beginning, Gary's one step ahead of you.

Almost immediately after that, Gary will challenge you to a Pokémon battle. If you win, you'll get money, your Pokémon will get experience points, and Gary will get mad. If you lose, go back to your house and your mom will heal your Pokémon for you.