First, determine the gate voltage you need. This will give you the ratio between A & B, since they form a voltage divider. Since your supply voltage is 18V and -9V below supply is well into saturation for any reasonable MOSFET, you can just set them equal to each other. That's easy, and it means you'll switch at similar speeds on and off.
In my diagram, I have 5VDC going through Resistor 'B' to the gate... it seems from this that you thought 18VDC would be going through resistor 'B'...
Given that I will be applying 18VDC to the Source and 5VDC where indicated, if I want to run 20mA through 4 LEDs which drop 3.2V per LED, what value of current limiting load resistor should I use? I don't know how to determine what Vds will be either.
From my understanding:
18V = 3.2V + 3.2V + 3.2V + 3.2V + V(load res) + Vds
If this is true, how do I know what Vds... after which I could determine the load resistor value (1 equation and 1 variable).
Also, how can I determine what values to use for Resistors 'A' and 'B' for a particular mosfet?
A run-down on how to calculate these things using values found in a mosfet datasheet would be awesome!