I've put together an example of this new API, read about it here: Example Yahoo Weather YQL to fetch forecasts and render with JQuery.
It looks like the examples have been updated and from what I could gather it is possible to make a request to a YQL URL and fetch the data without authentication.
So it's possible to execute a query like this just by sending it as a URL parameter...
YQL
select * from weather.forecast where woeid=1100661
...and get results back in the JSON format (or XML if you wish)...
The whole URL request looks like this:
URL
https://query.yahooapis.com/v1/public/yql?q=select+%2A+from+weather.forecast+where+woeid%3D1100661&format=json
All you have to do is URL Encode the YQL statement and pass it in using the 'q' URL paramether. The 'format' URL parameter specifies whether the weather data should be returned as JSON or XML. In case you are wondering, I looked up the WOEID here.
Of course you probably don't want to bring back all of the results so you can tailor that query using the YQL Console first...
I'm glad Yahoo has reenabled public access but it is definitely too late in my opinion as I would imagine many like myself have switched from this API to something like OpenWeatherMap.
-i