The aim of Professor Bubble is to collect as many points as possible. To get points you need to destroy the colored bubbles. In order to burst those bubbles you need to row/connect at least three bubbles of the same color.
In the bottom center of the gaming window you will find an arrow. You can change to direction this arrow points to with your computer mouse. Every time you click the left mouse button you will fire a new bubble to the current direction of the arrow.