Hopefully this won't confuse you even more, but I have posted the current 00z run of the GFS surface temp and dewpoint forecast for 123 hours (which is Tuesday night). The temp map shows isobars in black, wind barbs, and surface temperature. Perhaps this will help you see where the fronts are in relation to the colder/warmer air. You can also see the sharp contrast in the dewpoint map. Fronts are not analyzed on these maps, but you can easily see where the cold front is located by the sharp temperature gradient right through AL, TN, KY, etc. (temps are in the 60s ahead of it and in the 40s behind it) as well as the troughing or "kinks" in the isobars. Now you will also typically see a significant change in wind direction behind the front, but this system is a bit complicated so I won't go into why it's not on this one. You can also see that behind this strong low pressure system is a high pressure system with much colder air that is moving down from Canada.
By definition, warm fronts and cold front must extend from an area of low pressure. The reason is because it is the dynamics related to the low pressure system (as well as upper level forcing) that drives the progression of the fronts; a portion of this is the fact that low pressures are areas of lower level convergence (air wanting to move toward their center counterclockwise). High pressures are not associated with any large scale (synoptic scale) surface boundaries as they are areas of lower level divergence (air wanting moving away from their center clockwise). So basically you could think of especially a strong cold front as the leading edge of the high pressure system, which extends away from the center of low pressure. So as a high is moving off the coast, the wind on it's western or left side is southerly. This would then precede the next coming cold front and so on and so forth.
You are correct about the fronts separating 2 air masses. A cold front means cold air is advancing behind it (cold air advection). A warm front is when warm air is advancing behind it (warm air advection). But this is atmospheric and it's not always textbook pretty and all. Sometimes they are sharp and strong, other times they are weak and hard to pick out. I also have posted the graphs from my weather station from a strong cold front we had pass though last March. The temp plummeted after its passage; you can also note the quick jump in pressure and abrupt change in wind direction. To answer your other question of how you see the different air masses, really the only way to do that is to look at a surface temperature or dewpoint map, kind of like what I have posted from the GFS.
I would suggest reading through this article on wikipedia about cold fronts for a better understanding of them.
https://en.wikipedia.org/wiki/Cold_frontI know this was a lot
Let me know if I need to clarify anything!
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