Hey John,
The "shout" call can be found in the Places section of the documentation, because a person must shout from a specific place. The API call must be made as a PUT to:
https://v0.api.shizzow.com/places/{places_key}/shout
You can also send an optional PUT parameter of {shouts_message}, which may be up to 255 characters in length.
If a user is shouting through an oAuth-enabled application, Shizzow will record the application that is used to shout and will display that application within the shout output. You may add your Shizzow oAuth application at
http://www.shizzow.com/applications/add
Let me know if I can help in any other way.
Cheers,
Ryan