Use the mouse to aim and click to jump. Grabbing a jetpack will allow you to fly temporarily until the gas runs out or until you touch another star.
TIP: Aim slightly in front of the star you're trying to hit.
UPDATE: The highscores don't appear to work on Newgrounds. However if you want to post a score, play the version here: http://saricden.com/fgame .php?n=Starstream&h=400&w =700 (remove the spaces in the url)