Large airports have 2 ways of finding out the weather. There are TAF's(Terminal Aerodrome Forecasts) and METAR's (METeorological Aerodrome Report).
TAF's are generated usually by the meteorological office responsible for aviation in their country. These forecast the weather over usually a 24 hour period for a specific aerodrome.
METAR's are generated from at aerodromes either by trained observers or by automated airport weather stations. These are generally issued hourly or half hourly, if the weather changes outside certain limits between those times a special weather observation is made and issued.
As Fife Airport is unlicensed we don't have TAF's or METAR's, however we do use the TAF's and METAR's for Edinburgh, Dundee and Leuchars to help us get an idea of the weather around our local area.
Another available tool is Airport Weather which gives an automated METAR and TAF based on all available weather data. You can access our page here. Also on the page is a link to our webcam.
Screenshot from Airport Weather