I don't believe there's an easy way of doing it.
I used to live in a hilly area and was able to forecast the weather based on where the thunder was coming from, the wind, the smell in the air, the type of surrounding light, cloud cover.
Since I moved in the mountains, the signs have changed a lot.
But if you know the land features from the surrounding area, and generic weather patters, you could have an idea of what the forecast might be using wind speed, direction, change in temperature, types of clouds, and so on.
For example, in the summer, one can forecast rain by the change in the surrounding light. Rain can be smelled from long distances if the winds are right. Also, a change in humidity could easily be felt. Air feels heavier, wetter.
Same with snow. Clouds look heavy and it creates a certain bright glare.
Also, in the winter, clear night skies bring a cold night.
As I said before, it depends a lot on the location. These are just generic guidelines of what to look for.