I want to install OpenOffice. What can I do to install it on my computer?
As of now there is hardly any changes between LibreOffice and OpenOffice. The former is a fork to free OpenOffice.org from the clutches of Oracle.
Till date Sun has asked for copyright assignment to Sun if you wanted your patch to be merged. This has been a great deterrent and has limited community involvement.
LibreOffice says "Everyone is invited". It is not an office suit which will be controlled by one organization, but many organizations will take part to develop it. The supporters include Google, RedHat, Canonical, Novell and a few more (not sure about the list).
LibreOffice has also brought up a wikipage named "Easy Hacks" to get the community involved in the development. This is a great step as probably people would be excited to look at the code.
From that page I can see that the codebase is a bit messy. There are non-English comments, bogus comments, dead code and what not.
Another good reason for breaking apart was that Oracle does not look interested in taking the development of Open Source ahead. OpenSolaris is nearly gone and if this fork didn't happen, probably OO.o would also have become stagnant.
Starting with Ubuntu 11.04, openoffice.org packages are "transitional" packages facilitating migration from OpenOffice.org to LibreOffice. That is, they are packages that provide no actual files, but which have the corresponding LibreOffice packages as dependencies, so that LibreOffice gets automatically and smoothly installed.
Therefore, if you want to continue running OpenOffice.org instead of LibreOffice in Ubuntu 11.04 (or higher), installing Ubuntu's openoffice.org packages will not accomplish this. You will have to install OpenOffice.org from the packages provided at the official OpenOffice.org website. Before doing so, you should remove all the openoffice.org and libreoffice packages currently installed on your system, along with their global configuration files. The easiest way to do this is probably in the Synaptic Package Manager (as suggested by Uri Herrera). Mark these packages for complete removal. These packages' names are listed at https://launchpad.net/ubuntu/+source/openoffice.org and https://launchpad.net/ubuntu/+source/libreoffice (the lists overlap only partially, so check both).
Before you replace LibreOffice with OpenOffice.org, you should be aware that:
LibreOffice is currently a very close fork of OpenOffice.org. So any functional changes (including new bugs) you are seeing from the version of OpenOffice.org in Ubuntu 10.04 LTS or Ubuntu 10.10 to the version of LibreOffice in Ubuntu 11.04 are likely also to be present in the newer version of OpenOffice.org.
Once you install the upstream version of OpenOffice.org by running the installer obtained from the official OpenOffice.org website, OpenOffice.org will no longer be updated when you update the rest of your Ubuntu system in the Update Manager. Therefore, you will have to make sure it receives updates, and perhaps update it manually. It does have an automated mechanism for checking for updates, however. (I think this is in the Help menu.)