If you are the Network Admin, there will be a "Delete Case" link located beneath the [Alerts] tab.
If you are not the Network Admin, you will see a "Flag Case" link. There, you can quickly send a message to your Network Admin, then, they can perform the appropriate action on your behalf. Your Flag Case messages could look something like this:
"Hello [network admin], please delete the case for John Smith that added by mistake (DOB: 01/01/1950, C1234). Thank you!"
Here is a link to video you may find helpful: https://vimeo.com/97442551#t=420s