You can stream Elgato Game Capture HD video by using a 3rd party applications called XSplit and OBS (Open Broadcaster Software). 

Elgato Game Capture HD supports these streaming applications for Windows only.

By default, there may be an audio delay between what you are saying during streaming, into a microphone, and what's actually appearing in the video stream.  Your commentary may not exactly match the gameplay, unless you make a simple adjustment.

 

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Adjusting Audio Delay in XSplit Broadcaster

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Check to make sure you have XSplit Broadcaster version 2.3. You can download it from here:

https://www.xsplit.com/download

You will also want to make sure you have Elgato Game Capture HD software version 2.10.67 or higher for Windows.  The latest software can be downloaded here:

http://www.elgato.com/gaming/download

To adjust the delay:

1) Open up XSplit Broadcaster.

2) At the top, click on "Tools", then "General Settings":
3) In the General Settings window, click on "Audio".
 

4) In the Audio Settings, check the "Delay" box under "System Sound" and "Microphone" and set the value for both to 1450ms, which is the average delay of the Elgato Game Capture HD.

You may need to experiment to find the correct delay value settings, as different devices, computers, etc may affect the delay.

 
5) Once you have set the delay, click "Apply", and "OK".

6) If you are using a webcam, you will need to delay it as well, by the same amount as the microphone.

7) Right click on your webcam source in XSplit Broadcaster:
    8) Set the delay to the same delay as the microphone:

 

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