Let's start at the beginning.
There are two versions of Pokémon so far. The Blue version and the Red version. In Japan, there is a Red, Blue, Green, Silver, and Gold Edition, and even the 151st Pokémon, Myuu was given out to many Pocket Monster fans at Space World in 1997. With luck, perhaps we'll see these versions too?
You start the game as a 10 or 11 year old boy who finally came of age to become a Pokémon trainer. Every trainer's dream is to become a Pokémon master and obtain all 150 Pokémon. You can either choose to start out with:
-Bulbasaur, a grass Pokémon
-Charmander, a fire Pokémon
-Squirtle, a water Pokémon
You should choose Bulbasaur because it will fare the best for novice players. The primary goal is to defeat wild Pokémon in the field with your initial Pokémon, then to capture them with a Pokéball. They will start as as low levels, then you will slowly build their levels, and they may even evolve to entirely different looking Pokémon. Wild Pokémon can only be found in grassy areas. You know you'll be in one if it's waist high.
As you travel around the world in search of Pokémon, you will come across rival trainers. Trained Pokémon are tougher to beat then wild Pokémon. You can not capture tamed Pokémon ; they are loyal to their original trainers. When you beat another trainer, you'll get cash along with the Exp. Some people may even want to trade Pokémon with you.
Whenever you spot a Pokémon, whether in a battle in the wild or against a trainer, your Pokédex will automatically record it, even if you are defeated. Your Pokédex will only record it's cry and appearance, but it's statistics will not be filled until you actually capture one.
Probably the coolest aspect of Pokémon is the ability to play against a friend via Game Boy Cable Link. It sells at about $10 US if you need a new one, but one should've come with your Gameboy. Each version gives you about 139 Pokémon. You'll have to trade with a friend to get the rest.