1. Use one of these utilities for backing up your data to an external hard drive, and verify it is bootable.
2. Verify that your firmware is up to date.
3. Uninstall any third party hacks to the menubar or Dock if upgrading Mac OS X.
4. Uninstall third party utility programs.
5. Verify that your third party printer driver has been tested with the newer version of Mac OS X.
6. Verify that any software or hardware you have installed has been tested with the newer version of Mac OS X.
7. Repair permissions by opening Applications -> Utilities -> Disk Utility -> First Aid tab -> select boot hard drive you are going to install the upgrade on and repair permissions. Mac OS X 10.1 or earlier should upgrade to 10.2 first before being able to do this, though 10.1.5 has a repair privileges utility you can run.
8. Verify you have sufficient hard disk space for installation, and never let your hard disk space get under 3.5 GB free in case you need to Archive and Install Mac OS X to restore Mac OS X to its earlier version. If you have a backup of the original data that is a mirror backup as suggested in step 1, erasing the original and recovering from the backup is all that is needed, and you won't need to Archive and Install if the system was working before the update.