1) First we must uninstall QGIS and GRASS
sudo apt-get purge qgis*.* grass*.*
2) Download and install the Debian Squeeze version of the python-sip and python-qt4 for your architecture.
3) Block the installed version with the update manager. Go to Edit > Preference > Ignore packages:
4) Add the QGIS repository:
deb http://debian.gfoss.it/ squeeze main
deb-src http://debian.gfoss.it/ squeeze main
4) Update your system and install QGIS and GRASS.
sudo aptitude update && sudo aptitude install qgis grass grass-doc
Easy!