Clicking the Weather button will bring up the Weather window. Add cities for which you need forecasts; include country, state or province information to increase the likelihood of selecting the correct city.
For old iPods you can choose to have the weather forecast transferred as a Contacts entry or to the Calendar, where each day's forecast will be added as an event in the Weather Calendar.
For current iPods you also have the option of transferring to Notes. If chosen, your forecasts will appear under Weather.