There are a number of ways that a forecast may be produced ranging from simple to more complex and computationally demanding. Some of these are described here for ease of understanding how forecasts are produced.
The simplest method that is used in forecasting is known as the persistence method. This method simply takes into account the current conditions and makes the assumption that these conditions will prevail into the future. Therefore a sunny day is expected to be followed by another sunny day. This forecast works well for very short forecast periods but quickly fails once prolonged. However, it has also proven to be useful for long range forecast periods as well. The analogue method is one in which similar past conditions prevailing at the time are taken into consideration when forecasting for future periods. This therefore looks for similar situations in the past and the outcome from such a set of conditions. The difficulty in this method therefore lies in being able to identify similar patterns in the past records. What makes it a difficult technique to use is that there is rarely a perfect analog for an event in the future.
Forecasts on the 0-12 hour time period is called nowcasting. This type of forecasting requires some local knowledge and therefore requires a skilled forecaster than simply using the analogue method or computer models. It takes into consideration the prevailing conditions, such as wind and cloud cover, and looks at events that can happen quickly and in a small area (e.g. thunderstorms).
Numerical weather forecasting uses computer models to simulation the state of the atmosphere. They take the analysis as the starting point and evolve the state of the atmosphere forward in time using understanding of physics and fluid dynamics. The complicated equations which govern how the state of a fluid changes with time require supercomputers to solve them. The output from the model provides the basis of the weather forecast.
Although a forecast model will predict realistic looking weather features evolving realistically into the distant future, the errors in a forecast will inevitably grow with time due to the chaotic nature of the atmosphere. The detail that can be given in a forecast therefore decreases with time as these errors increase. There becomes a point when the errors are so large that the forecast is completely wrong and the forecast atmospheric state has no correlation with the actual state of the atmosphere. However, looking at a single forecast gives no indication of how likely that forecast is to be correct. Ensemble forecasting uses lots of forecasts produced to reflect the uncertainty in the initial state of the atmosphere (due to errors in the observations and insufficient sampling). The uncertainty in the forecast can then be assessed by the range of different forecasts produced. They have been shown to be better at detecting the possibility of extreme events at long range. Ensemble forecasts are increasingly being used for operational weather forecasting (for example at ECMWF, NCEP, and the Canadian forecasting center)