How does the computer's BIOS change the clock speed?
Many modern mainboards utilize a system of clock distribution based on clock syntesis. A quick example would be IDT/ICS chip like  ICS954101 (although I am not sure if this particular IC can change FSB, but as an idea). The main reference crystal is typically 14.318MHz, the rest (CPU FSB, DIMM, PCIe, USB, SATA, etc) are derived via PLL and are programmabe over SMBus/I2C bus. That's how some mainboards may have some frequencies tunable from BIOS, all depending on how "liberal" their BIOS is. 

Frequency of the system clocks is definitely independent of supplied voltage, the voltage on clock chip is well stabilized. But some board voltages may have an independent control via a different power management block, and the BIOS might have linked tables that allow higher clocks if higher voltage is set, for overclocking enthusiasts.