I don't understand the realationship between Resistors and Capacitors, but I have a solid understanding of Ohm's law.
I would like to start simple, and work my way up.

I understand resistors.
For resistors in series, the resistance is added.
For resistors in parallel, the equation is as follows.
Rt = 1 / ((1/R1) + (1/R2) + (1/R3)) etc.


So yes, I totally understand resistors. I even know the power dissipation, and the current. It's simply using Ohm's law.

Using the resistor values (resistance Ω) for each one.

R1 = 10Ω
Solve Power dissipated given 12 volts & resistance : (E² / Ω) = 12 x 12 = 144 / 10Ω = 14.4 Watts.
Solve current given 12 volts & resistance : E / Ω) = 12V / 10Ω = 1.2 Amps
Solve power dissipated given current & resistance : (I² x R) = 1.2A x 1.2A = 1.44 x 10Ω = 14.4 Watts.
etc. etc.

So I know a little about Resistors. It's the capacitors I need help with.

 

Here are some ideas to play with: Turn your resistors upside down...literally. Turn them into conductances. 1/1000 ohms is 0.001 Mhos, one millimho. Suddenly, resistors in parallel is so easy! It's just a bunch of conductances to add up. When you get done, flip them upside down again and you have ohms.

Then look at capacitors as conductance, frequency dependent conductance. For a given frequency, a larger capacitor has more conductance. If you want to add series capacitance, turn them upside down and pretend they are resistance (at some given frequency).

This isn't the whole story, or even the usual story, but it's an exercise that will get you through problems by the method of versatile thinking.

 

Another way to look at the frequency dependence of a capacitor is to consider it an open (infinite impedance) at DC and a short (near zero impedance) at the highest frequency you can imagine (blue light for example). If you were to graph the impedance of a capacitor as a function of frequency it would look like a hyperbola in quadrant I with the horizontal and vertical axes as asymptotes.