Step 1: The Basics
Step 2: Making Tetrises
Step 3: Strategies
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.