The easiest way to get started with Cython is to write your code in Python and then compile it with Cython. It also helps to look at examples, which are numerous (for example, over 100,000 lines in the [http://hg.sagemath.org/sage-main/file/59538ebc8f3b/sage/ Sage source code])
Most Python code will compile, though there are currently a few [:Unsupported: exceptions] to watch out for.
Once you have code running, you can make it faster by using the "cdef" keyword to declare types.
See the [http://sage.math.washington.edu/home/robertwb/cython/fast-cython-bis.pdf slides] given at Sage days 7 for a simple overview and some examples.