Well, i don't know if this is quite the website for this kind of subjects, but let's get on topic ^^
It really depends on the origin of the stream, many stream providers have a different way of delivering the video with different encryption aswell, so you would really have to be more specific... But you could probably google it anyway...
A solution that would always work is some screencapture software, but it's hard to find something that offers proper quality.
Use idm (Internet Download Manager) it is a powerfull downloader tool (fastest i should say) ...it can capture and download videos from any online streaming site...I personally use it a lot for downloading youtube videos.
For youtube i used keevid, it is free and it can also convert the video to mp3. If you are using android, you can use tubemate to download video from youtube using your android device.
For windows software client I use Internet Download Manager.