Provided some tips—like those from tetrisconcept—you can keep a game of Tetris going forever. All you need is a Tetris game that randomly generates piece sequences, a hold feature, and at least 3 piece previews.
Not all Tetris games work like that, though 'good' ones are supposed to (apparently). You might need to check if your Tetris fulfills those requirements. But if that's the type of game you have, you should check out this lengthy read about how to think about and game Tetris.
Here is a small snippet, which includes diagrams. Mind, the letters correspond to the piece that most looks like that letter. As in, "T" is, well, the T shape. Z is the piece that closest looks like a Z, and so on.
If done right, your play should look like this GIF:
Actually, for those of you that are more visually oriented, the GIF might explain patterns more rapidly, and without jargon to boot.
But if you'd like to read up on methods, again, check the full article out.
Playing forever [tetrisconcept, via Boing Boing]
You Can Keep A Game of Tetris Going Forever. Here's How.