How much bandwidth is your ISP providing to you? If it's at the lower end, say only 3-8Mbps, then that could be the problem. The person streaming video is consuming most of the already limited bandwidth. In a case like that, you may have to use a router that support QoS (Quality of Services) options to limit the amount of bandwidth available to any one individual client, thus providing more for other purposes.
Of course, it always helps to have more bandwidth from your ISP if you can afford it. Some the less expensive plans are only designed to support low-bandwidth applications (email, web browsing, etc.), not streaming.