Answer:
Meteorologists use a variety of observation methods to first assess the initial condition of the atmosphere, including satellites and radar, automated observation networks, and especially 12-hourly radiosondes (sent up in weather balloons). Using these observations, the future condition of the atmosphere can be predicted with the help of computer models (supercomputers), which incorporate extensive knowledge of atmospheric dynamics and premised around chaos theory (that the atmosphere behaves stochastically).
While computer models are absolutely necessary to "crunch the numbers" given the sheer number of calculations required, which are in the trillions, a skilled meteorologist is still needed to interpret model output. They do this with an understanding of the nature of the area for which they're forecasting, a solid foundation of atmospheric physics to know whether a model solution is indeed feasible, and past experience to know what has happened in previous situations when the atmospheric setup was similar. Computer models are only tools (they are referred to literally as "guidance" by meteorologists in shorthand), and cannot simply be read and used without skilled interpretation.