Check this diagram. The locomotive is moving to the right, catching up with it's own sound waves. The waves that reach the observer on the right are thus closer together. This makes the observer hear a higher frequency sound!
Since the sound it produces is radiating away in all directions, the train is also "running away" from some of it's own sound waves. The observer on the left perceives a "stretched out" version of the waves, and perceives a lower frequency!
Similar effects occur with light. As the light source in the diagram below moves to the right, its waves become closer together, and the light observed by someone getting closer to the light would be "shifted" toward shorter wavelengths, or bluer colors. An observer from which the source was getting farther away would perceive red-shifted light.
red shift
blue shift
Here's an online activity you can watch about Doppler effect. (You need the shockwave plugin for your browser)