How is a series resistor limiting the voltage for a diode?
The resistor is not limiting the voltage for the diode, the voltage on a diode can be considered as constant:


Source: Tutorialspoint.com

As you can see in the diagram, the voltage of a diode is kind of "fixed" around the specified forward voltage (around 0.7V for a normal diode, 1.8V for a red LED). If the voltage over the diode is increased further, the current is increasing rapidly. Without a series resistor this is exactly what would happen - the current increases and the diode burns up (if the power supply delivers more current than the diode can handle).
But with a series resistor there is a kind of "negative feedback": If the voltage over the diode would increase, the current would increase a lot. This higher current would create a higher voltage drop in the series resistor (U = I*R). And a higher voltage drop in the resistor means less voltage for the diode. Thus the resistor is effectivly limiting the current through the diode and only by that it is also fixing the voltage.