You will need the Forms permission to perform this action.
You are able to set a list of email addresses to be notified when a person submits a custom form. The email will contain responses for each field (including any that were left blank). If the form contained an email field, the reply to on this notification email will be set to that value (if provided).
Navigate to the form and select the "Settings" tab. Then select the "Notifications" sub tab. Finally, search for the people you want to add and select them from the results.
Once you have added all the people to the list, click on the "Save" button in the upper right of the screen to save your changes.