My question is how a game knows how much/what to load when they are starting up. First of all I'm assuming loading screens mean they're bringing data/instructions from the hard drive to the main memory and main memory to cache. So, does the developer specify what exactly is supposed to be brought in somewhere in the code? Do they assign priorities for the data if someone does not have enough RAM? How exactly does the game know to load more data on a 3GB RAM system than a 2, and does it then need to change the instructions to map to the proper address in the RAM to get that data?

the OS will manage the extra memory , and will use page files.
to know what to load , you read from a file( for example a script) what resources to load , then you know you need to load 666 resources , after each load you display the progress 1/666 , 2/666 and so on