Yes, even with an advanced mobile phone. Video files are like ordinary files that you upload to your (other peoples) server (and link to them). Nothing advanced there. I asked a related question:
Which digital (video) camera do you recommend?
I am not an expert on this, but seemingly there are no other members here either

that are experts. You may use tools like MS Movie Maker (follows with most MS OS's) or more advanced tools like
Adobe Premier Pro to edit the movie clips.
As far as I know, the best computer with the right software installed is
the Mac Pro.
So, until an expert enters the forum, I am WPW's selfproclaimed

expert on video and image manipulation, (scroll down the last link in my signature for additional information under the heading "PHP resources for image manipulation").
If you get the right tools and hire some young girls / boys with an open mind, you may start competing with Hollywood and Cnn. That may be the reason I did not get a single answer from over there

.