How do I erase/format a harddisk from a live CD?

From a live session start Gparted Partition Editor from System -> Administration:

Choose the drive you need to re-partition or format from the top right. Then select your partition (in this case /dev/sda1). By right click on the partition a menu pops up that lets you choose to Delete or Format this partition.

Partitions need to be unmounted before changing them

In case you install another OS it may be sufficient to just delete all partitions leaving the drive unpartitioned. Partitoning and formatting will then be done by the new OS's installer.

We have to keep in mind that private data on that drive will still be recoverable after deleting or reformatting partitions.