I'm confused about the single slit diffraction pattern. Why are light and dark patterns? Where is the constructive and destructive interference occuring if there is just one wave?
The wave interferes with itself. You can consider the wave to be composed of many smaller "wavelets" and these all add up to give the interference pattern. See the following article. http://en.wikipedia.org/wiki/Diffraction_formalism
So when doing the double slit experiment, one will see two diffraction patterns on top of each other then?
The most simple picture about diffraction comes from using the Fraunhofer case (both source and detection screen at infinity) and Kirchhoff's approximate formula. Then the diffraction pattern seen at the screen turns out to be given by the Fourier transform of the openings, i.e., the electric field is proportional to this Fourier transform. The physical picture behind this is that any point of the opening is the source of a wave, and at the infinitely far away screen you can approximate the spherical wave by a plane wave (Fraunhofer diffraction). You find the math in great detail at the Wikipedia link in GeneralOJB's posting.