The part of the tree that is most exposed to the cold and the sun will turn colors first. This happens for a couple of different reasons. The dark red/purple pigment is Anthocyanin, which mask the green color from Chlorophyll. The purpose for these pigments are to protect Chlorophyll, which is easily destroyed by too much light. They are produced more when there are low temperatures and lots of sunlight, thus the reason for production in the top parts of the tree first.
The yellow and orange pigments show up when Chlorophyll starts to break down when the tree gets ready to go dormant for the winter. This pigment is Carotenoid, which reflects yellow and orange light. They are normally masked by Chlorophyll. When the tree cuts the leaves off (a corky membrane forms between the petiole of the leaf and the stem, cutting off its supply of sugar). The rest of the Chlorophyll is used up doing photosynthesis, and then the Carotenoids show up, not being masked by Chlorophyll anymore. The leaves exposed to the most sunlight will use up all of the Chlorophyll first.
I hope that helps! I actually just learned about this whole process recently in my biology class.