How does resistance, voltage and current work in a circuit with a small load
It's very important to remember that Ohm's Law applies to the voltage across a resistor and the current through the resistor.

If you know the source voltage and the LED forward voltage then you can use Kirchhoff's Voltage Law to determine what the voltage must be across the resistor. Then you apply Ohm's Law to determine what value of resistance will result in the desired current, now that you know what the resistor voltage must be.