Python uses the database-independent DB-API for its database connectivity. For MySQL specifically, it uses the MySQLdb module. The latest version of the API (at the time of this writing) is Python Database API Specification 2.0. It's still a fairly new API, and many features available in other APIs have not yet been implemented. However, its simplicity makes it easy to learn and use.
You can find MySQLdb and full installation instructions at http://sourceforge.net/projects/mysql-python/.