We opened up a YouTube account and uploaded our video files there. You test them on YouTube to see they play okay. Once you are satisfied with them working, you can copy the embed code (click on the share option under the video you are playing) and paste the embed code into the footer of the question you need it to play on. Use HTML to position it correctly on the screen.
The embed code looks something like this ...
<object width="445" height="364"><param name="movie" value="http://www.youtube.com/v/cmwiTX9IYAT&hl=en_US&fs=1&rel=0&border=1
"></param><param name="allowFullScreen" value="true"></param><param name="allowscriptaccess" value="always"></param><embed src="http://www.youtube.com/v/hmxiTR9IVAM&hl=en_US&fs=1&rel=0&border=1
" type="application/x-shockwave-flash" allowscriptaccess="always" allowfullscreen="true" width="445" height="364"></embed></object>
Whilst you may not understand all of the code, YouTube does the dirty work by creating the nasty code for you. You just need to perform a copy and paste into your footer.
There are options within this embed code that allows you to perform certain options like hide the video control buttons, display the YouTube banner, etc.