There are plans afoot to put LibreOffice (the successor to OpenOffice.org) version 3.3.1 into the next release of Ubuntu, 11.04, Natty Narwhal, due April 28. However, you can have it now on Ubuntu 10.10. Johannes Eva outlines three options and shows how to do each one. His instructions are simple, clean and easy to follow.
I've taken the first option, installing LibreOffice in parallel with OpenOffice.org. It seems to install cleanly. One thing to watch out for: it will copy your existing OpenOffice.org setup into its own directory, .libreoffice. That's fine as far as it goes, but if you need to keep them in synch, that's your problem.