Firstly, go to the OpenOffice website: http://download.openoffice.org/ and download the Linux .deb file.

1 - Once you have done that, extract the .deb file,

OOo_3.2.0_LinuxIntel_install_en-US_deb.tar.gz
Then you'll see a file called OOO320_m12_native_packed-1_en-US.9483

2 - You can remove the existing version of OpenOffice if you wish with this command:

sudo apt-get remove openoffice*.*
3 - Copy and paste OOO320_m12_native_packed-1_en-US.9483 onto the desktop then open Terminal and paste this command:

sudo dpkg -i ~/Desktop/OOO320_m12_native_packed-1_en-US.9483/DEBS/*.deb
4 - Then paste this command:

sudo dpkg -i ~/Desktop/OOO320_m12_native_packed-1_en-US.9483/DEBS/desktop-integration/openoffice.org3.2-debian-menus_3.2-9472_all.deb
Once you've done that you'll find OpenOffice 3.2 in Office.