Dustin,
The models are mainly guidance used to compliment your forecast. They're like several additional forecasters you have at your disposal, but like other humans they have flaws that you need to be aware of. They're useful if you either reject or accept their reasoning based on your knowledge of the atmosphere. Reading the models without thinking critically about what they're saying doesn't help you understand more about forecasting. Today's bust in Oklahoma was a perfect example of the importance of not following the models blindly.
Most forecasting follows something called the forecast funnel, which is a method of forecasting used by many. To follow this method, you start at analyzing the hemispheric features (like longwaves and blocking patterns), then synoptic features (things like highs, lows, troughs, ridges, and fronts), down to the mesoscale (things like storms.) It's a way of assessing meteorological phenomenon by scale and helps you gain a full understanding of how the atmosphere is structured. After knowing the atmospheric situation now, you can start to look at how atmospheric features will change into the future. This is often how I attack forecasting problems. I identify the features and then think about the Problem of the Day (POTD). The POTD could range between what type of storms will form (this was a problem today in Oklahoma), when the storms will form, how much rain will a place get, etc. In most situations there could be more than one problem.
After identifying the POTD, a forecaster will use his own experience, knowledge of the atmosphere's 'rules', and the forecast models to try to solve that problem.
There are several things you can do to improve your forecasting. The first (and sometimes not most obvious) is practice. Achieving a feat like forecasting the weather isn't easy and you have to build experience. It takes being wrong and learning from your mistakes. Something else you can do (and are already doing!) is ask questions. Also, it's good to read things about it when you can, but be sure to try to apply what you've read. Be patient (this is something I had trouble with)! It takes time.
I highly recommend
http://www.theweatherprediction.com/ for beginners. I also started reading forecast discussions to become familiar with the language and terms. If a forecaster identified something on a map, I'd try to pick it out too. Tim Vasquez's books are also helpful too:
http://weathergraphics.com. Also, the University of Illinois has a great website that can get you started:
http://ww2010.atmos.uiuc.edu/(Gh)/guides/home.rxml
Hope this helps and good luck!