The tutorial is sparse, like a lot of the documentation for the C interface. When I was writing my modules I looked at the source of other modules (some in the standard library, some 3rd party) to see how they did the things I wanted to do.
Along these same lines, it can also be useful to take some Python code, run it through Cython [1] or Pyrex [2], and look at the generated C source code. I'm not trying to say they generate perfect code -- but I find it's often faster to check out generated source than it is to find the appropriate entry in the reference manual, or use it to figure out *where to look* in the reference manual, especially before you know exactly what you're looking for. ;)
-cc
[1] http://www.cython.org [2] http://www.cosc.canterbury.ac.nz/greg.ewing/python/Pyrex/