Download the Linux (deb) version to your computer. (I have a /downloads directory for this purpose.) You will have a file ending in .deb.tar.gz.
Use Archive Manager to open this file and extract the DEBS directory to somewhere convenient, for example /tmp/DEBS.
Open a terminal window, CD to the DEBS directory, and run
sudo dpkg -i *.deb
You’ll probably want to make a desktop launcher for it, because it doesn’t install into the menus (this is good, because it can co-exist with an earlier version of OOo on your computer). The program is installed into /opt/openoffice.org3 (for the public beta) or ooo-dev3 (for the developers’ builds). Look in the /program subdirectory for soffice.