You wouldn't use Facetime for this, but rather Quicktime Player which is also installed on your machine. Open QT and choose File->New Movie Recording and you will see a window with the input from your camera and microphone. Once you are ready, click the record button and go. The resultant video will be in MOV format and depending on the length of it, quite large. Play around with the recording times to figure out how big the files are and how you want to break them up if they become too large.
Either way, you'll likely have to employ some sort of a cloud sharing service (Dropbox, Box, etc.) to share the files with someone else. Another option is for you to upload them to a video sharing site like Youtube or Vimeo and not make it a publicly indexed video but share the specific link with people.