1) Before you do anything, burn any critical data to optical media (DVD+R should work well).
2) If you do nothing more, at least do this: Create a complete backup of your current system, preferably by creating a bootable clone on an external drive. (SuperDuper and Carbon Copy Cloner both offer this function for free.) If your installation goes horribly wrong, you can get back to normal in the time that it takes to reboot or clone back from the external drive.
3) Search for Application Enhancer files (which may have been installed by other programs) and eliminate them to avoid the possibility of the Leopard "blue screen of death".
4) Disconnect all peripheral devices from your computer, except for the mouse and keyboard. This means all USB and FireWire devices, such as printers, scanners, hard drives, iPods, modems, etc.
5) If the Mac you're upgrading is critical to your livelihood or well-being, verify that your must-have software and peripherals are Leopard-compatible by checking the developers' web sites (or phoning them) before you install.
6) Resist the temptation to upgrade when you are facing a tight deadline or are in the middle of a crucial project.
7) For the best odds of success, use the Archive & Install option rather than the Upgrade option to avoid the chance to bringing corrupted files into the Leopard system.