Ok, watch this movie (quicktime!) for a practical example of how to embed a player in your website.
You always need to have the player and the media file hosted (a simple webhosting plan will do).

A few things to note:
This is a screencast from dvcCast, a Mac OS encoder that everyone on a Mac should check out IMHO. However, this is just how they get the h.264 file; you can use Vegas for that (or anything that generates compatible flash files)
It shows you how to use Flowplayer, similar to Jeroen Weijerings player. The same principles apply.
Don't be phased by unfamiliar terms like CyberDuck (an FTP app) or TextWrangler (text editor).

Josh also shows you how to use features of Flowplayer to easily use it on forums and in e-mail.

George/