I have a canon S3. How can I take a video and send via email to my family?

Answer 1

I do not know your type of camera, therefor general instructions.

Canon normally has a setting for video on the selector on the camera, (one setting for automated, one for manual, one or more for preselected settings, and one or more for video.)

If you set your camera on that setting you push (the button you would normally push for a photo) once to start and once to finish taking the video.
Next you upload, as you do with photos, to your computer.
Once on the computer you can attach it to an e-mail. But video fragments are big, so they might be too big for an attachment or block their in-box if they use a small size or phone-in connections.
If that is the case you can use a big file website, like: http://www.mailbigfile.com/
They will get a message that a file is waiting for them.