I have installed mysql server using
$ sudo apt-get install mysql-server
then I installed python-mysqldb using
$ sudo apt-ge
Your code snippet is fine. So the problem lies with getting libraries to match up. Here are some tools to help track it down... but do post back to let us know how this worked out for you:
$ python --version
Python 2.6.6
$ easy_install yolk
$ yolk --list
DecoratorTools - 1.7 - active
MySQL-python - 1.2.2 - active
...
$ pydoc -p 8080
pydoc server ready at http://localhost:8080/
$ python
>>> import MySQLdb
>>> help('modules')
Please wait a moment while I gather a list of all available modules...
ArgImagePlugin _bytesio exceptions pyexpat
BaseHTTPServer MspImagePlugin cProfile multifile
MySQLdb ....
$ dpkg -L python-mysqldb
/usr/lib/pyshared/python2.7/_mysql.so
/usr/lib/pyshared/python2.6/_mysql.so
Note the Ubuntu package installs mysql to several python versions.