If the client uses Windows, you can use Windows Media Encoder at the remote location and Windows Media Services at the data center.
For Linux, there are a few choices.
(not sure if they support video yet).
The gist of streaming from a client site:
You send one stream live or pre-recorded to the data center (where bandwidth is cheap and plentiful) and then distribute to the world from there. If you're using a shared hosting service, inquire if they offer additional streaming services. For extremely large user bases, you start getting into content delivery services like akamai and the likes, but based on your question I'm assuming that is out of the scope of this discussion.
Then you have a few options, content viewers can either watch the streams live (push) or can watch at a later date (pull).
Video requires a lot of bandwidth, so you'll need to look at what quality the video will be and how many concurrent users will be watching to accurately determine your needs.
lowest quality watchable 500kbps
VCD bitrate is around 1100kbps
HD bitrate is between 8-20Mbps
Those would be per viewer.
Sidenote: Make sure the client is sitting down before you explain the bandwidth costs associated with delivering high quality video to a decent sized audience.