How to embed our own videos on a page?

I’m working with some clients on upgrading their site to WordPress. (I’m still somewhat new to WP and learning as I go; I used to do everything by hand in HTML.) They have several videos on their existing site and would like to be able to embed them in various pages, like they have done here:

http://scs-matters.com/debra-bio.shtml

The videos reside on the same server as the rest of the site. Is there an easy way to embed them in a similar manner in a page using WordPress? I’ve read this page in the Codex but the stuff at the end about oEmbed Discovery is a bit over my head.

http://codex.wordpress.org/Embeds