To delete a contact is simple. Go into the contact and underneath their name at the top-left there will be a red link called "delete contact". This will display a warning to confirm if you wish to delete. Clicking the green "Proceed" button will then delete the contact. Be certain that you wish to delete any contact, as their data will be completely unrecoverable.
If a contact is currently assigned to a "Completed" plot and you attempt to delete their contact, this will display a second warning. Note that if you proceed to delete a contact assigned to a completed plot, it will remove all customer data applied to the plot. This cannot be recovered.