Hello, and welcome to the Pokemon Basics Guide. Here, in my pokemon pre-school, you will learn about the wonderful world of pokemon without all of the confusing technical terms which used to annoy me when I first started (I'm afraid that you will have to learn some pokemon vocabulary to understand the world of pokemon). 
Pokemon
Pokemon is short for pocket monsters and the first games were Pokemon Red & Blue, then Green, but when the games were translated for the UK and U.S, Pokemon Green wasn't there. But, Pokemon Green is exactly the same game as U.S Pokemon Blue. Almost.
Pokemon are mythical creatures and they are separated into 17 different types. There is also the ??? type, but that is not overly important (even though anything with question marks is always important !). They are mainly found in the long grass, but some are found in the really long grass, caves, ponds, the sea, on certain types of tree, with the pokeradar which is an item found later in your adventure (on Pokemon Diamond), with a fishing rod or, in the case of some elusive pokemon, in certain places (eg. legendaries). Pokemon can evolve to change form (it doesn't take millions of years !) and can level up by gaining exp (Maximum level is lv.100). They can learn moves (also called attacks or techniques when they level up or by TM or HM (technical machines and hidden machines respectively)
The Story
You start off in your home town and you somehow go and find a suitcase of pokemon (it depends which game you are playing). Suddenly, you are attacked by wild pokemon and you must use the pokemon you chose to defend yourself. The professor will invite you to his lab and tell you that you can have the pokemon. He will also give you a pokedex to record the pokemon that you have seen. You will then proceed to undermine the plans of an evil team, beat all of the gyms and finally defeat the elite 4. You will also have a rival who will challenge you multiple times during your adventure.
If you are playing a non-nintendo portable game, like Pokemon XD on the Gamecube.
Once you have beaten the elite 4, you will be presented with a national pokedex which you can record more pokemon with (you will not be able to gain the national pokedex in some pokemon games).
You can also catch pokemon called legendaries at certain points in your adventure. All legendaries are incredibly strong and they know really good attacks.