Assuming that all your networked machines are part of the same workgroup with sharing enabled and working between them. Also, using the Authenticated Users option, rather than adding "Everyone" will be more secure but may not allow for free access from remote locations.
It's safer to share only the C:>Users folder rather than sharing from the actual drive letter. But it's your network and you should know who is logging into it.
To share the entire drive:
Open My Computer -> right click Local Disk C: or preferably the C:>Users folder or which ever drive letter your drive is using ->Right click and select Properties -> select Security tab -> click Edit button -> click Add button -> Type> Everyone in the open box and hit OK, this will give access permissions to every user who is part of the Workgroup. Put check marks in the boxes for full access and control as required -> click apply OK etc. -> click OK -> wait while permissions are set -> and your Done.
After that click on the Sharing tab then click the >Advanced Sharing button, put a check in the box to share the drive, then click on the permissions tab, then use the check boxes to allow Everyone full access as required. Hit the apply button on both windows.
You should now be able to access the new drive from the Vista machines at which point you should be able to send your back ups to that drive.