1) Open the Activity Stream, click on the share icon (Record must be selected before clicking)

2) A popup box will appear and you will be asked to fill in email IDs of people with whom you would like to share the record

3) After entering all email IDs, click on the submit button. An alert will appear informing you that the record has been shared successfully. 

Your selected contact, who is outside of the organization, will now be able to access the record.