Certain objects/floors of the screen will flash, and depending where it was most on the screen (to the left, right, up, or down) is the direction you hit on the joystick. If your sword flashed, then the action button was hit.
This was significantly improved upon in Space Ace 2 and Dragon's Lair 2.
In the first Dragon's Lair, there was quite a bit of trial and error mixed inter-mixed with the "move toward the flash".. (I don't think Dirk's sword ever flashes in the first one)
I discovered a continuity problem:
Lizard king room: You're supposed to be chasing after the pot of gold that's stolen your sword. But as you're running, look at your belt.