Saucer hunting was, essentially, the degenerate game play that base Asteroids reduced down to when you were playing for score.
The game was to leave a last, single, small rock floating about, and wait for the fast, 1000 point saucers to show up.
The trick was that the saucers were very fast, and very accurate. So the solution was to essentially hold down the thrust button, and race from bottom to top (since the ship rolled over the edges, rather than bounced off).
When a saucer showed up, you had to quickly react, point the ship in the right direction, just a bit off axis, and blast the saucer with a stream of bullets.
I was never particularly good at that myself, but my friend was. That's how you got on the high score boards in the local arcades back in the day.