Much of weather magic can be divided into two major parts. One part is invoking precipitation (rain, snow, sleet, etc.) and one part is driving precipitation away. Growing up on a farm, I have an intimate knowledge just how important precipitation is for the growth cycle of plants and the water cycle. I remember when there was a drought of some significance in my area when I was small. Tensions ran high among the farmers because everyone's crops were at risk the longer the drought continued. Even the farmers with livestock had concerns because the pasturage they were using to feed their animals was suffering from the drought and producing less feed for their cattle, horses, and pigs.
One of my clearest memories of this time was of my grandmother shaking out the dust from her broom in the backyard. It was something that struck me as odd. I asked her why she was doing it and she just smiled. I also remember my aunt storing her broom upside down, with the bristles pointed towards the ceiling (a thing that just wasn't done most of the time). Not long after this business with the brooms happened, we had drought breaking rain. A storm system popped up over the Great Lakes and blew in with soaking rain for the whole region. It was years later, when I was reading about weather magic in my research of folk magic, that I stumbled upon a description of housewives shaking their brooms in the air and storing them upside down to invoke rain during the pre-Industrial era out in the rural places where folk magic was still fairly widely practiced.
There is the practice of hanging out washing that was wrung to nearly dry to invoke rain as well. It is like the comparatively modern one of washing your car on a dry day. Hanging out things to dry or washing your car to summon rain is not as effective as the broom method, from what I have seen. They are, however, less conspicuous than someone waving a broom around in the air. Another practice is reciting a prayer for rain (to the deity of your choice) while shaking a rain stick. This was one that my mother used on a regular basis.
In many ways, the same practices work for summoning snow. I have also found success in tossing a small handful of white ashes up into the air while praying to the gods for snow. Invoking snow is also possible through tossing finely cut pieces of paper in the air while saying a similar prayer. The falling ashes and paper resemble the snowflakes and act to draw the snow to you.
Timing magic to draw precipitation can be tricky. Greater success comes on humid days than dry ones. It is also easier to draw precipitation when the moon is waxing or full.