Multiple methods. Some based on observations of what’s happened in the past when various observations were similar(cloud types, air pressure, humidity, temperature, etc.) some based on models of the physics that govern weather.
When sunlight hits the surface, much of it is converted to heat, and if any moisture is present, more of it can evaporate into the air as the temperature rises. Now, this hot air is also less dense than cold air, so it wants to rise. As it rises the pressure drops, which causes the temperature to drop(adiabatic cooling). The air is now too cold to hold on to all the moisture it absorbed at ground level, so it forms clouds, and if there’s enough humidity, rain. The air then slowly radiates its heat out into space before sinking back down.
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