In Mac OSX 10.5 through 10.7, the procedure for resecodeing a user's password in single user-mode has changed slightly, so I put up some quick reference notes here:

NOTE: This procedure does NOT work for OSX 10.8 Mountain Lion
  1. Boot into single user mode (press Command-S at power on)
  2. Type mount /
  3. Type launchctl load /System/Library/LaunchDaemons/
  4. Type dscl . -passwd /Users/username password, replacing username with the targeted user and password with the desired password.
  5. Reboot ( shutdown -r now )