There are many different fields in meteorology. A theoretic or dynamic is a meteorolgy finds a mathematical description for the weather patterns. The synoptic looks at a larger area in order to forcast it. Applied meteorology looks at problems for biological, aeronautical and agricultural.
NWP needs some of the most powerful supercomputers to create an accurate model.
Blue Marble
To predict weather for the future meteorologist use different methods such as trends and the analog method. To predict using trends meteorologists look at direction of fronts, high and low pressure centers and other variables. Then they make their best guess to where and how fast the front will come or if it will come. To predict with the analog method meteorologist look at past simmiler weather patterns in years past.
But the most popular method is the numerical weather prediction (NWP). This method uses computers which use both methods of tends and analogs. One of the most know weather prediction model is the GFS (Global For?ecast System), which was developed by Natioinal Oceanic and Atmospheric Administration.