Arduino: How does one extend the pins to accommodate multiple sensors?
There is no true way to expand pins, but there are techniques you can use to exchange processing power and data for more effective pins. 

Using just 3 pins and 1 chip select (slave select) pin per device you can talk to many devices over SPI (serial peripheral interface).]1

If the devices you want to talk to do not support SPI you can use other ICs such as a shift register that talks to over SPI and give you more effective digital IO.


The above picture shows an example of two 8-bit shift registers daisy chained together. Using 3 pins from the microcontroller you are able to control 16 LEDs.

You can multiply this effect even higher using a technique called multiplexing. Instead of using shift register outputs directly, you can attach components into a grid and "select" a column and row.



In this case an arduino using 3 pins is able to drive two 16 shift register outputs which can drive 64 devices. This is essentially how a keyboard works.