Start the eMac with your original OS X System Restore disc: insert the disk and restart the eMac while holding the C key.
At the OS X Utilities screen, select Disk Utility from the Utilities menu. Erase the disk and select the "erase free space" option. The single pass (fastest) method is sufficient for all but the most sophisticated, expensive, and time-consuming data recovery methods.
After the disk is erased, you can either reinstall OS X from the System Restore disc or simply supply the disc to the new owner along with the Mac.
Many options. Use a USB flash drive, portable hard disk drive, FireWire Target Disk Mode, or network the two.
If you have a new Mac, use Setup Assistant but boot the eMac in Target Disk Mode and select "From a Time Machine backup or other disk" and not "From another Mac". The reason is that Mountain Lion will not communicate with a Tiger Mac using Setup Assistant or Migration Assistant, but if you use FireWire Target Disk Mode the eMac will appear as a locally mounted volume, just like any other disk.