Scientific Linux was designed so that an administrator can easily upgrade their computer between minor releases.
It is not required that administrators upgrade their release, because the security errata will be updated for all releases. But there are often features and/or packages included in later releases that were not available with the earlier releases.
Below is the steps, for both yum and apt, to change to the latest release. You can use either yum or apt to do the upgrade. Yum is prefered. Note that for the x86_64 installations, apt does not work.
These instructions are for updating between minor releases, such as from 3.0.1 to 3.0.3. Changes between major releases 3 and 4 (such as from 3.0.2 to 4.1), cannot be done with yum or apt, but must be done with the main installer.

Special Steps
Some steps will have one or more of the following markings. Only do these steps if your machine falls into the marked category.
301 : For systems that are upgrading FROM S.L. 3.0.1.
AFS : For systems that currently have openafs installed.

YUM

For The Impatient

1. rpm -Uvh ftp://ftp.scientificlinux.org/linux/scientific/30x/i386/misc/RPMS/yum-conf-30x.SL.noarch.rpm
2. yum update yum
3. yum upgrade

For those a little more cautious

1. Make sure you have done your backup's.
   I haven't heard of anyone needing them, but don't you be the first.
2. Make sure you have enough disk space. In particular, make sure you have enough space in /var/cache, which is where yum downloads the rpm's to.
3. yum update
   This will get your system up to date with the latest packages. It will also make the last step smaller. If you want, you really can skip this step.
4. yum clean all
   This cleans up all the rpm's that you just downloaded, clearning up your disk space.
5. rpm -Uvh ftp://ftp.scientificlinux.org/linux/scientific/30x/i386/misc/RPMS/yum-conf-30x.SL.noarch.rpm
   This will install the latest yum.conf for your system. If you customized your yum.cron, or your yum.cron.excludes files, these will not be touched.
6. yum -d1 update yum
   It's always good to have the latest yum before doing this, just incase the latest yum has fixed some bug you would have ran into. This also will download all the headers quietly.
7. 301 rpm -Uvh ftp://ftp.scientificlinux.org/linux/scientific/302/i386/SL/RPMS/sl-release-3.0.2-9.2.noarch.rpm
   Between 301 and 302 the sl-release rpm was changed from i386 to no-arch. Because we have exact-arch set for upgrades, it does not get updated with everything else. Because of the danger of turning off exact-arch during the upgrade, we felt it was best to simply update this rpm by hand.
8. AFS Check to make sure your version of yum is at least version 2.0.7-7.SL. If it isn't, then you need to run the command.
   rpm -Uvh ftp://ftp.scientificlinux.org/linux/scientific/303/i386/SL/RPMS/yum-2.0.7-7.SL.noarch.rpm
   
9. yum upgrade
   Note that this is a yum upgrade and not a yum update. If there is any package that 'obsoletes' another package, it will get installed and remove the obsoleted package. An example of that would be xmms-mp3 obsoletes xmms-mpg123.
10. Check your grub and/or lilo settings. Although yum usually get's things right when it updates kernels, it is always a good idea to give the grub and/or lilo config files a check.
    Please note that because your kernel get's updated before sl-release, your grub and/or lilo setting will still say they are for the older release. You can the title line on grub by hand to be whatever you wish and it won't affect anything.
11. yum clean all
    This cleans up all the rpm's that you just downloaded, clearning up your disk space.
12. /sbin/reboot
    Reboot into your new kernel and Scientific Linux release

APT

For The Impatient

1. rpm -Uvh ftp://ftp.scientificlinux.org/linux/scientific/30x/i386/misc/RPMS/apt-sourceslist-30x.SL.i386.rpm
2. apt-get update
3. apt-get dist-upgrade
4. apt-get upgrade-kernel

For those a little more cautious

1. Make sure you have done your backup's.
   I haven't heard of anyone needing them, but don't you be the first.
2. Make sure you have enough disk space.
3. rpm -Uvh ftp://ftp.scientificlinux.org/linux/scientific/30x/i386/misc/RPMS/apt-sourceslist-30x.SL.i386.rpm
4. apt-get update
   
5. apt-get dist-upgrade
   
6. apt-get upgrade-kernel
   
7. Check your grub and/or lilo settings.
   Please note that because your kernel get's updated before sl-release, your grub and/or lilo setting will still say they are for the older release. You can the title line on grub by hand to be whatever you wish and it won't affect anything.
8. /sbin/reboot
   Reboot into your new kernel and Scientific Linux release