Converting TopoDS_Shape to internal format

I'm new to OCCT. I'm trying to use it to read an IGES file and convert it into the internal data structures of the software package that we write. I think I've figured out the code to read the IGES file into a TopoDS_Shape object. I can use Shapetype() to see which TopAbs_XXXX type this shape really is. From there, I'm kind of stuck.

I figured out how to pull the X/Y/Z coordinates out of a vertex and edge, but I can't figure out how to get the geometric details from any of the more complicated shapes so that I can convert them into our software package's internal data structures. I think the types I need to convert are COMPOUND, COMPSOLID, SOLID, SHELL, FACE, and WIRE.

Can anybody give me some pointers on that?