Hubert,
First of all, you need an API key, you can find in the API documentation how to get one.
Then look at some samples how to build the URL, first check in a browser (Chrome or Firefox) if you get the desired result and then use the Web component to get your data.
The app I made was for a forecast on my current location, using the LocationSensor, and I used XML, which, I just found has a very different API from JSON for OpenWeatherMap.
I think the XML has much more straightforward set of keywords in its response, and after using call Web1.XMLTextDecode or call Web1.JsonTextDecode, you get a list of lists, which you can search through using "look up in pairs" from the list blocks.
You can find in the API documentation of OpenWeatherMap, for example how to get a 16 day forecast, there is also a list of available cities, which, after some searching, I found here:
http://bulk.openweathermap.org/sample/You will get a g-zipped list in JSON. You could load it as an asset into your app, and search for it when you need it.
Cheers, Ghica.