There are many different ways to approach usability testing for websites. The following video is a great example of a moderated, in-person test. The key to this method is that it allows you to create a local recording and provide guidance to the user when necessary.
This video by Steve Krug shows a detailed demo of a live usability test of a website. He starts off by getting the participant on the site and gathering initial impressions. Afterwards, he presents the user with a task and observes them as they run through it.
Interestingly, Krug provides a short quiz at the end prompting video watchers to come up with their own list of usability problems, before presenting his own. One issue he brings up is the extra value plan was unclear because the site did not convey that information clearly.