LÖVE

You don't need a "platformer" thing, just use a matrix and check below each bottom block in each part that falls. Anyone feel free to correct me on this.

No, you're correct.

Check here for the gameplay details, some stuff is really relevant to your code, e.g. the wiki page about "SRS".
http://tetris.wikia.com/wiki/Tetris_Wiki

I agree that the whole thing might be a bit difficult for a first game though.

Just out of boredom I've attempted to write a Tetris clone during the last 4 hours or so, I started without any concept and before I found the WiKi, so what I did is most likely totally wrong, against the rules and inefficient.
Anyway here is how far I came, there's no collision detection between Tetrominoes and no scoring system yet.

space = rotate
cursor keys = move and drop

I also decided to make a Tetris, here it is.
http://love2d.org/forums/viewtopic.php?f=5&t=34029

Hey, I know I'm a week late replying to this post but I am a newbie here so thought I would have an input. I started on tetris a while ago but came across some difficulties so I haven't had time to finish. Just wanted to say thanks to vitaminx for the tetris wiki link, thats pretty helpful, the article sets it out nicely and looks easy to follow. Just thought I would contribute something for all those tetris fans which is a tetris font, its pretty funky http://www.fontsaddict.com/font/tetris-blocks.html It may come in handy for some of you whether your into making things interesting..

Anyway, thanks again and talk to you all soon.
Katie