I can't find the QGIS installation path in ubuntu 12.10
A quick way to check is to type which qgis - it will give you the path as was stated above: /usr/bin/qgis
QGIS gets installed to /usr. It is lauched by a shell script, /usr/bin/qgis.
The location is
/usr/lib/qgis. In there you have the 'plugins' directory, if you need to add a plugin manually.