First, download the10.5.8 Combo Update here.
http://support.apple.com/kb/DL1324
Disk Utility is in Applications>Utilities. First
verify the drive. Select the volume you normally boot from, which unless you renamed it, will probably be named Macintosh HD. If the message you get says everything is OK, then and only then, hit the Repair Permissions button for the same Volume. If errors are reported, then you will have to boot from the Install Disc (or a clone if you have one) and Repair Disk from there. See "Try Disk Utility" for instructions.
http://support.apple.com/kb/TS1417
Here's what I do for a major update. Maybe not all completely necessary, but I like the extra margin of safety. _The idea is to have a good, error free 10.5.8 in place before you install Snow Leopard._
1. Have a backup so if something does go wrong, you won't be left in big trouble.
2. Verify and if necessary repair the drive from Disk Utility. (To repair, you must be booted from the Install Disc or an external clone.)
3. Disconnect all peripherals except the keyboard and mouse.
4. Download the Combo Update. It's generally more reliable to update from the standalone than from Software Update, and the Combo, as it includes all updates from 10.6 onwards, may correct any files that have been corrupted or somehow gone AWOL (missing.)
5. Boot in Safe Boot. Hold the Shift key down at start up. Give it time, it will take longer. (The Safe Boot will also actually check and repair the drive if necessary--and if possible.)
6. Repair Permissions from Disk Utility while booted in Safe Boot.
7. Install the update from Safe Boot. Keep all Applications closed.
8. Restart when prompted and give the system up to five minutes to finish the final touches of the update with all Applications closed.
9. Verify the Drive and Repair Permissions again.
10. And then I like to restart a second time.