You can specify who the alert notifications are sent to by supplying either Recipient Users, Recipient Groups, or both.
The buttons 
and 
can be used to add users or groups t the list of recipients for the alert notifications;
After clicking on 
a window titled "Add User" will open;
At the "Domain" prompt specify the domain of the user, then at the "User" prompt type in the users' name then click 
, and the specified user will be added to the list of recipients that the notification will be sent to;
The same process can be used with groups to send the notification to all members of the selected group (or groups).
You might want to tick "Send a carbon copy to the initiating user" if you want the user to be notified as well.
Finally, click "Save" to save this new alert