Usually, when you make your forecast, several hours will have elapsed since the numerical model run was first initialized. During that time, the atmosphere has evolved, storm systems have moved, precipitation has fallen. Have things happened the way the computer model has predicted they will happen? If the atmosphere's doing one thing, and the model expected it to be doing another, then you'd better not make a forecast based on the model, because it's already wrong!
Three things to compare to a model forecast are the surface map, satellite imagery, and radar composites.
Surface maps are useful for looking at the distribution of surface temperatures and the locations and speed of fronts and storm systems. Compare the 12-hour forecast of surface pressure and temperatures or surface wind and precip to the most recent available surface map. Focus on the area upstream from which tomorrow's weather systems will be arriving. You may be able to identify errors in magnitude (too hot, too cold) or timing (front ahead of schedule or behind schedule). These errors are usually systematic, which means that you can expect them to persist into tomorrow's forecast as well.
Satellite imagery is useful for looking at storm systems offshore and for identifying the location of upper-level features. Aside from the more obvious techniques of looking at visible or infrared imagery to see where the major systems are located, a useful tool for assessing the accuracy of upper-level forecasts is the water vapor imagery. This product, which will be discussed more fully later, tends to show large contrasts or areas of dryness (darkness) in the vicinity of upper-level jet streams or mobile troughs.
Radar composites are very useful for comparing the actual distribution of precipitation to the forecasted distribution of precipitation. As in the other comparisons mentioned above, errors in position or intensity are frequently apparent, and these errors can usually be expected to persist. Beyond this, the radar composites show structures on a much smaller scale than the forecast models can simulate, and so you can use the radar maps to infer the character (widespread, a few intense cells, etc.) of an area of precipitation that the model is forecasting.
Suppose you are forecasting for a city along the Rocky Mountains and your forecast depends on whether upslope precipitation is going to develop overnight. What would be the most important thing to look at?