How do I know where to place resistors on my circuit?

It is true that, in most conductors, the actual charge carriers are negatively charged electrons, which leave the negative terminal of the power source, pass through the circuit, and return to the positive terminal of the source.

However, early scientists studying electricity didn't know about electrons, so arbitrarily declared that current flowed from the positive terminal of the battery, through the circuit, reeturing to the negative terminal of the battery. Today, almost everyone uses this "conventional" (positive charge) current, and you will avoid confusion by using it also.

Circuits work equally well whether you wish to think of them using conventional (positive) or electron (negative) current.

For your LED and resistor circuit, it doesn't matter which component is connected to the positive terminal of the battery, as Kirchoff's Current Law says that the current is the same at all points in a series circuit. That is, the resistor will limit current through the LED, whether it is placed "before" or "after" the LED, regardless of which way you think the current is flowing.

You don't need to think of the current or the power "starting" at one side or the other of the power supply. Current flows in complete circuits, it doesn't start or stop at any particular place along the loop.

In particular, when two parts are placed in series, that means the current through them is equal, and the voltage across the series combination is equal to the sum of the voltages across the two components. These are basic implications of Kirchoff's Current Law and Kirchoff's Voltage Law.

In your specfic case, it doesn't matter whether the resistor is placed on the cathode side or the anode side of the LED. It will limit the current through the LED to the same value either way.