Streaming on xbox 360 you will need a capture card there are a few that you can choose from:
Dazzle DVC (std def)
HD PVR (HD)
AVer Media capture card
so these will capture the sound and video to a computer, then you will need a streaming software to push the video/sound onto a streaming site like twitch.tv :
xsplit (which is paid for)
OBS (free)
I would recommend OBS, there may be other streaming software but I have only used these two before.
Also your laptop may need to have a good processor and ram to stream if the laptop does not you will witness frames dropping, stream lag etc
let me know if you need anymore information!
char