What's the intuition for reading transistor/resistor circuits?
What's a step by step way of thinking about the flow of electrons in such a circuit? How can we tell it would provide constant current for instance?


The first step is to forget about flow of electrons. Think about conventional current flow from positive to negative or ground. This is the way we (nearly) all do it and why we draw the positive rail at the top of the schematic. Understanding electron flow has its uses but not for general circuit analysis. Note that the arrows in diode and transistor symbols both show the direction of conventional current.



Assume that both transistors are off initially.
Now figure out what might get turned on. It's not going to be T1 initially as there is no current to the base. T2 has a feed to its base at (1) via the 2.2 kΩ resistor so it will turn on.
As T2 turns on current will flow from the collector and through R. The LED will start to glow.
The voltage at (2) will now start to rise. When it gets to about 0.6 or 0.7 V T1 will start to turn on.
T1 turning on will start to steal the bias from T2 and the circuit will settle with 0.7 V across R. If the voltage on R goes up T1 will steal more bias. If it goes down T1 will turn off a bit.
The current through the LED will be \$ I = \frac V R = \frac {0.7} R \$.