One quick way to achieve this is to select the plane and add a new material, in the material settings under shadow, enable Shadows only.
then enable transparency, use Z Transparency and use the alpha slider to control the strength/darkness of the shadow.
To further enhance this, you can enable Ambient Occlusion and use a blend sky. It is also worth noting that the shadow you get is dependent on the type of lamp settings you use, in the image below I am using a sum lamp with ray shadow enabled.
