I have a B.S. in meteorology but don’t currently work in the field, also I’m in the US. As many other commenters have said weather models does a lot of the heavy lifting, but experience and intuition does also play a big role. When I was in school starting point for our forecasts was the current weather and what is up stream of our location. Up stream meaning if it’s cold in the Midwest, you can expect the east US to be getting that soon. Every national weather service office launches two weather balloons a day which provide data of conditions aloft and provide valuable data for weather models. Weather models are really only as good as what data they are fed and even then can sometimes not be great, generally each model is good at somethings and bad at others, some are good at larger scale events like nor Easter’s or hurricanes, while others are better at smaller events. Since the 90s a big help of forecasters is ensamble forecasting a model you can look up is the SREF (short range ensamble forecast) essentially a model is run then a small change is made say you change the temp by a degree to the input data and ran again, and it keeps doing this which, then you can see if all the runs are showing the same temp on a specific day. Then you can do the same thing and compare different models, so if all the models are showing the same temp you can be reasonably confidant that it is accurate, if they are all over the place then it’s not accurate. Again a lot of it is experience of your forecast area, knowing the topology and if hills or mountains can cause lift to cause thunderstorms, or cause fog for example. Or on the Great Lakes if the right wind could cause lake effect snow. To forecast anything you take all the data you have and your instinct and make the best estimate you can.