Many people will tell you that Tetris is a great game, but you may be thinking, "What's so great about putting shapes together?" Well, I have the answer!
Step 1: The Basics
In Tetris, you have seven tetraminos to put clear lines with. Once you complete a line, it is cleared and all of the blocks above it fall down. Tetris has an odd gravity. When lines are cleared, every block moves down an equal number of grid spaces to the lines that were cleared. They don't fit into spaces to make chains or anything, they may just float in midair.
Step 2: Making Tetrises
Making Tetrises is the name of the game, literally. Making a Tetris means clearing four lines in a row, the maximum that can be cleared. As pictured here, the way you do this is to build up blocks into a stack of four lines except for one column of blocks. Then, when you get a stick/line/straight piece, you can drop it in the slot and get a Tetris!
Step 3: Strategies
There are many strategies that master Tetrisers use. Here are my favorites.
The T-Spin: This only works on the newer games, such as Tetris DS. When you get a T block, but the space has a block well, blocking it, you can wedge it into a space while you spin it. On Tetris DS, you can get a bonus for clearing with a T-Spin. T-Spin example
The Infinite Spin: This one is simple. It buys you time so you can think about what to do next. Just get a piece that can rotate, and rotate it forever until you find a good spot.
The Hard Drop: This one is easy too, but you can benefit greatly from using it, especially in multiplayer. On Tetris DS, Tetris Worlds, whichever one is on the N64, and various others, pressing up lets you perform a hard drop. The tetramino goes straight down into a space, no questions asked. This can also be your worst enemy if you abuse it or get too excited or something.