If you want the custom form to be sent to specific email addresses (e.g. all of your site admin people), you can add their email addresses when you create the form. As you are building the form, click on "Email notifications" and add all of the desired email addresses, separated by commas: http://en.support.wordpress.com/contact-form/#notification-preferences
As far as I know, there isn't a way for the person submitting the form to automatically receive a copy. This seems like a nice feature to be able to add if you want it (perhaps with a sentence for the user like "Check this box if you would like to receive a copy of this form via email"). I'll tag this thread for staff attention to see what they think about the idea. :)