Making an API request is as easy as making a basic http request. The best way to try out a request is to use your browser. Each request's specification page will contain an example link and an example of the xml you can expect to get back.

Each request will require that you send your developer id. You can obtain your developer id by setting up your Developer Profile if you have not already.

http://www.livevideo.com/api/GetFeaturedVideos.ashx?
            developerId={My Developer Id}