From the Start screen, swipe left to display the Apps list. Alternatively, tap All apps (located in the lower-right; may require scrolling to the bottom of the Start screen).
Tap new (located at the bottom).
From the 'To' field, enter a 10-digit mobile number. Alternately, enter a contact name. As the name is entered, a matching contact may appear and can be selected at any time. Alternately, tap the Plus symbol (located in the upper-right), tap a contact then select the appropriate mobile number (if applicable). Repeat this step as necessary to add additional recipients.
From the 'type a text message' field, enter a message.
Tap attach (located at the bottom).
Tap the appropriate video folder (e.g. Camera Roll, Saved Videos, etc.)
Tap the desired video.
Tap send (located at the bottom; to the left of 'attach').