Here you go Chris. Thunderstorms develop from 3 ingredients which are moisture, instability and a lifting mechanism. Supercells require one more ingredient which is shear.
Here are some basic things I look for on any given day that I might chase.
MOISTURE: This is the very first thing I look at on the day of a possible event. Obviously, the higher the dewpoint the better, but I like at least a Td of 55 or so for starters. A Td of 55 here in Amarillo is ok, but it's nothing to write home about. A Td of 55 in NE New Mexico around Clayton is fairly significant. With everything else being equal, the more moisture you have in the atmosphere, the higher the instability will be.
A dryline is simply a boundary between hot and dry air to the west, and warm moist air to the east. The dryline is usually set on the 50-55 degree isodrosotherm. A dryline is very significant on a storm day because it is the possible burst point of convection. This is because of the convergence on the dryline. The air to the west of the dryline is usually from a SW direction and the air on the moist side is usually from a SE direction. When these winds collide at the surface, they can't go down into the ground, so they must go up. If the winds are strong enough, and all other factors are in favor of storms, storms will form.
INSTABILITY: Like I said earlier, everything being equal, the more moisture in the air, the more unstable the atmosphere will be. Usually instability is calculated by Convective available potential energy (CAPE) and the Lifted Index (LI). Also, the higher the temps at the surface, the more unstable the atmosphere will be. Now, up in the mid layers of the atmosphere, you want cold, dry air. Remember that as long as the parcel of air is warmer than it's environment, it will continue to rise. So, in conclusion, a nice setup to have would be this. Warm, moist air under cold, dry air.
LIFTING MECHANISM: A lifting mechanism is anything that will lift the parcel of air to it's level of free convection (LFC). After it has reached the LFC, it will continue to rise as long as the parcel is warmer than it's environment. Here are a few basic lifting mechanisms.
COLD FRONT
WARM FRONT
DRYLINE
TROUGH
OUTFLOW BOUNDARY (In basic terms, a small cold front)
WIND SHEAR: Wind shear comes in two forms. They are speed shear and directional shear. Speed shear is the speed of the winds in the atmosphere. You want to have higher winds at 500mb than you at the surface. Here is an example. A wind speed of 20 kts at the surface and a wind speed of 60 kts at 500mb will tilt the updraft of a storm. You want this because the tilting will essentially keep the updraft going because it will not get suppressed by precipitation. The precip will drag air downward in the updraft and will offset the rising air that will keep the updraft going.
Now, directional shear is very important for mesocyclones and eventually tornadogenesis. You want to have veering winds as you go higher in the atmosphere. Say, SE winds at the surface and SW winds at 500mb. Now, suppose you have 20 kt SE winds at the surface and 60 kt SW winds at 500mb. The 500mb winds are stronger than the surface winds, so they will create a horizontal roll to the surface winds. Here is an example. Put a rolling pin on a counter facing North and South. The rolling pin represents surface winds of 10 kts. Now, take your hand and place it on top of the rolling pin facing an east west direction and think of your hand as 500mb winds at 60 kts. Obviously, your "hand is the stronger wind at a 90 degree angle to the rolling pin, so what happens to the rolling pin now? Well, it starts rotating on a horizontal plane. Now, take a thunderstorm that forms and lifts this horizontal plane into the vertical. Now you have a rotating updraft and a mesocyclone. As the mesocylcone strengthens and stretches vertically, the rotation gets stronger. Think of a figure skater. When he or she rotates, what happens when they bring their arms in close to their body? They rotate a lot faster. (This is why a lot of very tall, skinny tornadoes spin like a drill bit at the surface. A great example is the Arnett, OK tornado on 5/4/07). This is what happens when a mesocyclone stretches...it gets smaller in the vertical and tightens up, and when everything is just right, a tornado forms.
In my opinion, I think a lot of people get too "involved" with forecasting on a particular day and fail to look a the big picture. These "ingredients" that I discussed are the foundation to a possible tornadic supercell. Keep it simple and I think you will have a lot of success. If you haven't already, I highly recommend that you thoroughly read this site from top to bottom:
THE WEATHER PREDICTION
NOTE: I do not claim that everything in this write-up is exactly right. If I said anything that is wrong, please discuss, as I still have a lot to learn myself!