Let me explain how i did the upgrade:
1- As NoobieDoobieDo says remove the previous version of the Open Office. To do so open the Mandrakelinux Control Center. Then choose the "Software Management" and from there choose "Remove". Search for "open office" and you will see "OpenOffice.org-1.1.3-0.20040820.9mdk". Select this package and click "Remove". The Control Center will prompt you that there are some related packages and they should be choosen too. So click "Ok". It will automatically select all the related packages and press "Remove".
Open Office 1.1.3 is gone.
2- You probably downloaded a <openoffice version>.tar.gz file from www.openoffice.org.
Right click on that file and choose "Actions > Extract Here".
3- Open a terminal and sign in as a root. (type "su -" press Enter and type your root password and press enter again).
4- Go the the folder where the <openoffice version>.tar.gz is extracted to. (That folder is in the same place with that .tar.gz file and has a similar name to "OOO680_m3_native_packed-2_en-US.8968").
5- Type "cd RPMS/" (take you to the RPM folder).
6- Type "rpm -vi *.rpm" (install all the rpms).
7- Type "cd desktop-integration/ "
8- Type "rpm -iv openoffice.org-mandriva-menus-2.0.0-3.noarch.rpm" (I see that you are using Mandrake 10.1)
9- Type "openoffice.org-2.0" (This will take you through a registration process)
10- And for last I would suggest you to reboot your machine to get rid of the old menu items.
I know the importance of a "step-by-step" guideline when you are a newbie. I tried to be as clear as it is possible. I hope I didnot miss anything. Good Luck!