Once again, great questions! For the purposes of keeping this thread on the topic of "Monday's Storm" I'll try to answer with a real life example on that.
But first, based on the kinds of questions you've been asking, and the fact that you work in computers and loved the Skywarn Program, I can say you're probably a good candidate for meteorology class.

In case there is anyone else who's been following our exchange and asking similar questions, I'll offer some tips on finding weather education around here (and then I'll relate this post to the thread topic, I promise!)
R2B told me of a certificate program at Penn State, and a lot of TV weather people (including Kelly LaBreque on ch. 6 Portland and several at the Weather Channel) have done the cert. program in Broadcast Meteorology at Mississippi. I believe both are correspondence programs.
If you would like to take something a little less involved, The
Mount Washington Observatory now offers a 2-month program in White Mountain Meteorology, in conjunction with NH Comm. Tech College in Berlin. They also offer themed "EduTrips" to the summit, and "Mountain Weather" is one of the themes.
In our local universities, UNH offers both an intro-weather and an intro-climatology course within their geography dept, and both are available for outsiders through the Dept. of Continuing Education. Plymouth State University has a similar intro-weather course, and you could probably also find one at Daniel Webster College since they have a big aviation science program.
Now... about the models... Cooking analogy: If a master chef sees someone measuring a certain amount of flour, sugar, milk, etc., he might say to that person, "I can see you're about to bake a cake." He COULD be wrong -- but he's a food expert and he's pretty sure he sees a cake coming together, and he's probably right.
The meteorology computer models are programmed to have the knowledge of the ultimate chef when it comes to weather. There's so much to memorize, and the equations for mixing those ingredients and predicting "how much the cake will rise once it's in the oven" are so complicated that very, very few people were even able to do them when they first came out around 1900. We had to wait until the early 1940s for a computer that could (the first computer-aided weather forecasts were KEY in helping the Allies win in Europe.)
Up until the mid-1990s, the models spit out reams and reams of NUMBERS. Paper maps. Black and white. Hear the dot-matrix printers giving you a headache... that was a weather office back then. Forecasters had to take colored markers and pens to their maps, just to make them easier to look at.
Then came the graphic revolution-- web pages with photos on them. Then web pages with flash video on them. Digi-cams that have 8.2 megapixels, on sale at Wally-World for $88.88. This graphic revolution made it so forecasters don't even have to print out maps anymore, because the weathermaps are multi-colored JPG files on the screen... and they're not just showing the ground; they're showing everywhere from the ground up. Click on a point within the atmosphere, say, 6,000 feet over Dallas, Texas. The model will tell you what it expects the weather to be right at that point, from now until next week. Then you can move your mouse up level after level, up to where the 747's fly, and get the same info.
Here's the part that makes it hard to forecast: The slightest change in humidity, barometric pressure, temperature, etc. in any one of those points on the 3-D grid can have a drastic effect on the weather in the middle of a city far away, several days later. The best illustration I ever saw for this concept was on The Simpsons, when Homer traveled back in time, accidentally stepped on a butterfly (though he'd been warned not to change *anything*) and when he traveled back to modern-day Springfield, his family were at the dinner table eating with tongues like frogs.
The models see various ingredients at every altitude from the cars up to the jets, and they say, "Given this present situation, and everything we know about the laws of physics, and everything we know has already happened, what will happen from this point forward?"
They've gotten to the point where they're accurate for "tomorrow" most of the time, and they're accurate "10 days from now" SOME of the time. Back in the 1980s, a 10-day forecast was unheard of -- that's how far they've come.
How does a weatherman know when a model is probably wrong? Two ways-- one is scientific, and the other is purely human. The most basic example of SCIENTIFIC: Let's say you install a computer program that allows Microsoft Windoze to tell you what the temperature is in your driveway. If it says the temp is 34 F but your driveway is icing up, you know the program is a couple degrees off. Your knowledge of physics (that water freezes at 32) has told you to disregard your computer's opinion this time. Granted, doing this with "The Models" requires a much greater knowledge of physics AND your local weather's typical behavior.
Now for the HUMAN example. When I was an EMT a few years ago, we had a guy and his wife stop into the station because he was having some minor chest pains and they didn't know where the hospital was. My paramedic partner and I checked this guy out 100%, and couldn't find anything wrong with him, even on the EKG. Scientifically, he was fine as far as our instruments could tell. But I looked at him, there was a look in his eyes I'll never forget. The way his skin felt. The way he talked. Something didn't feel right. The patient's wife and my partner and I conferred privately. I said there was something I didn't like, but couldn't explain. My partner said that was reason enough to find the hospital. We gave the wife directions.
We brought another patient to the hospital several hours later, and the nurses found and congratulated us for sending the couple in. He'd was beginning a major heart attack, and if he'd waited much longer he would've died. He was scheduled for emergency bypass surgery and expected to completely recover. How did we know that would happen? It wasn't scientific at all, just a feeling based on our 5 (and maybe 6) senses. Sometimes it happens that way, and meteorology is no different.
As for Monday (sorry this has been so long winded!) the basic ingredients are dry, cold air from Canada... Warm, moist air from the Gulf of Mexico... and some Atlantic coast moisture.... an air mass ("frontal") boundary hanging off the east coast to serve as a clash point/storm track. The ingredients are set to collide off the SC coast, or thereabouts.
It's a very, very, large-scale version of what happens when you steam up the bathroom with a HOT shower on a morning when it's below zero and you open the window. You get warm moist air forming clouds around your curtains, and maybe even some frost on the window screen.
On a slightly larger scale, Gunstock's snowmaking dept. does it too. They mix water with compressed air to make more of a water-vapor stream instead of straight water. The temperature has to be cold enough. The shoot their man-made stream of water vapor into the cold air and watch snow come out of a hose.
The basic snow equation is that the more extreme the ingredients are, the bigger the snowstorm will be. Coldest arctic outbreak ever + Hottest/most humid tropical heat wave ever = biggest snowstorm ever. Or, if a category-5 hurricane from the equator meets extreme arctic cold over NH.... we the skiers & sledders can only dream about that for now!