The creation of each part is controlled by the genes. As the genes change the part is made differently. As long as the change gives a survival advantage the change spreads throughout the population by breeding.

"Are you saying that these mutations are sort of independent of the larger organism? "
Would a mutation that changes your eye color do anything to the rest of your body? Probably not, but it still might give a small breeding advantage.

"And so any benefits caused by that mutation to the entire organism is just by chance?"
yes mutations are random. More often than not they hurt the organism.