openSUSE currently comes in two different release versions Tumbleweed and Leap
Zypper is the openSUSE equivalent of apt-get in Debian based distributions. On this page some of the basic functions of zypper will be explained (as I, or others, learn about them!)
The advantage of zypper over apt-get is that generally the repositories contain bleeding edge software and so those who wish to keep up with the latest versions of applications will find it very simple to do so. Also zypper always checks the repositories for the latest software and so it is not necessary to preface each installation or upgrade with an "update".
Repositories may be enabled in zypper but the easiest way to enable repositories is to use YaST (Yet another Software Tool) which is OpenSuse's GUI central command system covering control of software and hardware.
sudo zypper refresh && sudo zypper up
Perform Distribution Upgrade
sudo zypper dup
Install Individual Programmes
sudo zypper install <programme name>
Now here is a real gem. This is openSUSE's rolling upgrade programme, so that you can keep your version always attuned to the latest stable release. This is different from the "factory" version which still contains instabilities. All you need to do is to ensure that the Tumbleweed repository is the one from which zypper draws its upgrades.
The easiest way to install Tumbleweed is to follow the instructions on this site: 
Here is a summary of those instructions:
First ensure that you have openSUSE 11.4 installed. You should have these four key repositories installed as a matter of course:
* openSUSE 11.4 oss * openSUSE 11.4 non-oss * Updates for openSUSE 11.4 * Packman for openSUSE 11.4
Remove the following repos if you have them installed "Packman 11.4" ATI and NVIDIA.
Next install the "Tumbleweed" and "Packman Tumbleweed" repos. You do this by typing the following two commands once you have su-ed and have administrator privileges.
zypper ar --refresh http://download.opensuse.org/repositories/openSUSE:/Tumbleweed/standard/ Tumbleweed zypper ar --refresh http://ftp.uni-erlangen.de/pub/mirrors/packman/suse/openSUSE_Tumbleweed/ "Packman Tumbleweed"
In this case the "Tumbleweed" and "Packman Tumbleweed" that you find at the end of the command are the aliases of the repos, the http bit is the location, --refresh tells zypper to refresh the repository and ar tells zypper to add the following repository.
Or you can install them using YaST and specifying the locations of the two repos thus:
Once you have installed the two repos, then you can begin the dist-upgrade using the Tumbleweed repo.
This you do by typing:
zypper dup --from Tumbleweed
and answering the questions that arise. Hint: The correct answer is usually "y".
This will upgrade your system to Tumbleweed. You can then run:
zypper dup --from "Packman Tumbleweed"
to upgrade the rest of your software to the Tumbleweed version.
You can now add back in the NVIDIA and ATI repos if you have hardware that needs these using YaST.
Subsequently simply do the dist-upgrade to keep your distribution up to date with the latest version of OpenSuse.