How to make a constant current source
I don't understand current sources! Batteries are voltage sources, but
  how does one actually implement a current source?


Here's a current source circuit that uses an op-amp: -



This type of current source relies on Vset being applied to the non-inverting input of the op-amp. Due to the op-amp having a massive open-loop gain, the inverting input can be reasonably thought to be at the same voltage as the non-inverting input. The op-amp achieves this with negative feedback - its output drives a transistor until the voltage across Rset equals Vin. Hence current out of collector is: -

I = \$\dfrac{Vset}{Rset}\$

There are many more types of current source that produce similar results BUT the load resistance has to be within a limited range. Zero ohms is OK but trying to push 1mA through a 10k resistor on a 5V supply won't work.

On your picture, Iref can come from anywhere - an external signal or a resistor connected to a power supply - the I ref current is easily calculated because M1 acts as a low impedance with a volt drop across it - it's better to look at the equivalent BJT circuit because the volt drop is clearly "0.7V" when base is tied to collector.