Yeah, I wasn't sure what kind of answer you were looking for. OSM provides exports of the street data which gives you the ability to either:

A. Run a pre-existing routing program on it, such as http://wiki.openstreetmap.org/index.php/Rana, or

B. Write your own (which would require knowledge of algorithms such as http://en.wikipedia.org/wiki/A*_search_algorithm)

There are also services where people do these things for you, and for low volume, they might not mind if you programmatically scrape their results. A good example is http://www.batchgeocode.com/

Properly, Rana isn't intended as a package for programmatic access, but it does include code which does what you want:

* http://wiki.openstreetmap.org/wiki/PyrouteLib - Pyroute is probably exactly what you want.

* Rana's routing module: http://wiki.openstreetmap.org/wiki/Rana/Modules#route