Make sure this user has admin privlidges. Then Log out of the current account and log into the one you just created. The go to system preferences - accounts and select the old account and press "-".
Velmonk-
You can reset the main user password if you have a Tiger or Leopard bootable DVD. Just boot to the disk (press down "C" at startup) and use the utilities menu in the menu bar at the top of the screen once it's booted to the disk.
KFOG-
If you want to completely kill your disk, as I said to Velmonk, boot to an OS X install CD, and launch Disk Utility from the Utilities menu and follow the instructions listed here (ignoring the chart at the top) for secure erasing a drive.
If it's individual files you're looking to erase, then you can simply put them in the trash, then from the FINDER menu at the top press Finder > Secure empty trash