I have blogged the installation of OpenOffice 3.1 on Ubuntu 9.04 a few months ago.
OpenOffice 3.2 is not available on launchpad at the moment. Download it from the OpenOffice Website or use this direct links instead.
Extract the file after download and install the paket: (Uninstall old version of OpenOffice if you have already installed version 3.0 or 3.2 !!)
tar vfx OOo_3.2.0_LinuxX86-64_install_de_deb.tar.gz sudo dpkg -i OOO320_m12_native_packed-1_de.9483/DEBS/*.deb sudo dpkg -i OOO320_m12_native_packed-1_de.9483/DEBS/desktop-integration/openoffice.org3.2-debian-menus_3.2-9472_all.deb