You've never watched gameplay footage on YouTube? Awwww.
Well, you control a main character, Olimar, and he whistles the pikmin to his bidding. There are 3 types of pikmin (red, blue, yellow), and they each have their own gameplay attributes. Red are stronger for fights, and can be thrown farther. Blue are the only ones you can take under water. Yellow can carry explosives. Just think of the Pikmin as resources just like any old RTS for PC. You can only have 100 at a time on the field with you. You grow them by making them carry these coloured pellets to the respective coloured thing that makes Pikimin seeds come out. They have 3 phases of growth, or you can pluck them early and feed them nectar to make them grow to their subsequent phases.
The main story is that Olimar gets the help from these little guys to carry missing ship parts that have been scattered over the land, so Olimar can go back home. There's also a time limit, one for each mission where you have from day break until it starts to become dark where you have to run back and save your Pikmin from the dangers of the night wild life, and the other limit is that you have 30 days to collect all ship parts or at least the minimum required. A lot of people complained about the limits of the game, so in Pikmin 2 they decide to change the game to no limit on how many days it took you to collect things. That's what I like about Pikmin 1, the limitation.