Unfortunately we don't have a precise answer for this. Broadly speaking, there's at least three ways you can integrate a web cam into a web site:
1) Use a program such as DCN CamRunner. This will automatically take a picture with the web cam at an interval you specify, and will upload it to a web server via FTP. In WebEasy, you can put a placeholder image on your page, then use the "Link to Embedded Image" option to specify the URL of the live image file. When you visit the site, you'll see the latest picture. The catch is that you'll have to reload the page to see an updated image. This can be automated using a Java applet such as AnfyCam, which will just automatically refresh the image.
2) Use a program such as WebCam2000 - this will turn your computer into a mini web server for serving cam images. You can then put a placeholder image in your page which links back to a URL on your computer. This only works if you are directly connected to the internet via broadband, and you may have issues with dynamic IP addresses and such. Further, the security conscious might not be too keen on having people connect directly to their own computer rather than a separate web server.
3) Dedicated streaming media servers such as those from RealNetworks can be used to stream live video. I have no experience with these, other than that they cost a lot of money to install. However, various hosting providers will already have such software installed and should be able to provide more information.
Option 1 is the easiest/cheapest/most flexible, but it's not quite a "live" feed - depending on the speed of the connection between the web cam PC and the server, the absolute most you want to update it would be once every 15-20 seconds or so. Basically, you want to have enough time for the image to be sent to the server in between refreshes.