Please be kind, I am an electronics nub.  This is in reference to getting an LED to emit photons.

From what I read (Getting Started in Electronics - Forrest Mims III and Make: Electronics) electrons flow from the more negative side to the more positive side.

In an example experiment (involving a primary dry cell, a SPDT switch, a resistor and an LED) it states that the resistor MUST be connected to the anode of the LED.  In my mind, if the electrons flow from negative to positive, wouldn't the electron flow run through the LED before the resistor; thereby making the resistor pointless?

The resistor can be on either side of the LED, but it must be present.  When two or more components are in series, the current will be the same through all of them, and so it doesn't matter which order they are in.  I think the way to read "the resistor must be connected to the anode" as "the resistor cannot be omitted from the circuit."