The easiest way would be to just use a paid service to handle the video delivery. The big guys in that space are Brightcove and Ooyala. Expect to pay tens of thousands, especially if you want custom authentication. Viddler is a new interesting option that is trying to penetrate the market and might be a good fit. That said, you can probably more effectively buy than build in this space -- it is pretty complex, and there are lots of fixed costs (delivery) and it is a pretty technically difficult problem. Moreover, the services make it alot easier to monitize your content as they connect with ad servers and provide analytics, which are even more of a bear to effectively build. Finally, in 2012, mobile is key and I'd rather not solve the problem of mobile-friendly transcoding and mobile delivery myself.
If you do need to build it, you'll probably want to look at using a streaming server such as Flash Media Server of Wowza in conjunction with a CDN (Akamai or Limelight come to mind) to deliver the bits. IIRC, most streaming servers have some authentication bits you can ride. You would most likely have to integrate your authentication store over a web service of some sort.
Finally, if you haven't caught the drift, there is no such thing as low cost when it comes to effectively delivering non-public video. For public video use Youtube.
