There are three components to being able to fully understand a forecast discussion. These components are knowledge of the terms used, viewing the relevant meteorological data discussed, and understanding a full integration of atmospheric processes. Let's take a look at each of these components.
A forecast discussion is loaded with terminology. Highlight each term or phrase in the discussion that is unclear to you. The next step is to find out what the term or phrase means. You can contact me for an answer if you run into any terms that you do not understand. In the Weather Prediction Site, I have developed a glossary of terms from forecast discussions [click here]. Many terms in the forecast discussions are abbreviated. Make sure you understand these abbreviations.
A forecast discussion will often reference products such as the models, satellite images, radar images, Skew-T data, MOS data, and surface charts. It is wise to take a look at the charts and models referenced. First, it will help clarify what is being discussed and second it will grow your meteorology knowledge. Reading forecast discussions does not replace the crucial relevance of looking over as much meteorological data as possible. One goal should be to be able to eventually write your own forecast discussions.
The coursework in meteorology prepares you to understand the important processes occurring in the atmosphere. The weather is like a puzzle. Each bit of weather data adds another piece to the puzzle. With enough data and enough experience at examining weather data, you will have enough pieces to see the "big picture" of what is going on in the weather.
Here is where forecast discussions are available on the web:
http://www.weather.gov/view/states.php (click graphical next to state of interest, then click forecast discussion)