So click on the laser button once to bring up a list of presets and twice to make a basic laser on the screen.
The small square boxes on the ends of the laser are its starting and finishing points. Once you get into more advanced lasers, you can do other stuff with them, but for now we'll stick with this.
The laser is probably too big for what you want, so use the "start width" and "end width" bars to adjust the thickness of the laser. In case you get confused, the start is the box placed by default on the left, the end is the other one.
Move the laser to where you want it to start.
(To make it move in a straight line) Go to the frame where you want the effect to end and move the boxes to where you want them.
Playback. You'll see the laser start at its designated beginning and move on to the last keyframe.
For better tutorials (although there's no laser tut), clicky