(Hover over any image to view its description.)
General Technique
Stacking Evenly
Having a stack that is too uneven can make it very difficult to place incoming tetrominos in such a way that it doesn't waste space. The image below is a good example of an even stack, which allows each tetromino to fit in nicely.
Piece Preview
As you get comfortable with placing tetrominos, you'll want to get acquainted with looking at the 'preview' window (typically labelled 'next') beside the playing field. That way, you can get a sense of what piece(s) to expect after the one you're using. With enough play time, you'll be able to make quick decisions about where to place your tetromino based on what tetrominos are coming next!
Hard Drop / Soft Drop
A soft drop is simply speeding up the downward motion of the tetromino that is currently being played. Later iterations of Tetris introduced the hard drop, which places the tetromino down instantly to where it's positioned horizontally.
Unlike the hard drop, a soft drop allows the player to rotate or move the tetromino for about a second after it has landed.
Advanced Techniques
Stacking for 'Tetrises'
Clearing four rows in a single drop is known as a 'tetris', and rewards a lot of points for the player. The line piece is the only tetromino that can accomplish this. It's helpful to set up a stack (or two separate stacks) in such a way that a single tile gap is present somewhere in the playing field.
Combos
Combos are a particularly powerful tool in multiplayer games, as well as any Tetris games which reward combo chains with extra points. A popular setup for very long combo chains is the 4-wide, which can be seen in the clip below.
In the above clip, you can see professional Tetris battle player Wumbo (left side) get a 24 combo against another player playing Puyo Puyo.
Puyo Puyo Tetris is a
crossover between the Puyo Puyo and Tetris puzzle games.
The T-Spin
Some games reward players with bonus points for twisting a tetromino into a tight space. When this is accomplished with a 'T' Tetrimino, it's called a T-spin.