How do I figure out the number of layers required for my design?

Use just 1 or 2 Layer PCB for the regular boards and 4 Layer PCBs for interfaces with controlled impedance (USB, Ethernet, LVDS). If you study the component datasheet, various component manufacturers suggest a similar layout guideline pointing out to the support of minimum layers and the number of signal and ground or power layer depending on the power supply and dielectric isolation requirement.