(Disclaimer: I've never actually tried to read CMOS circuits, and I'm still far from an analog electronics expert. The tutorial itself has been vetted by people who worked on the simulators though -- thanks to Lidnariq, Quietust, and BigEd!)
The basic logic elements tend to be more involved in CMOS, which makes use of symmetrical pairs of transistors with different doping. (Roughly, the doping determines whether a high or a low voltage "closes" the transistor.) Compare the implementation of a NOT gate for NMOS and CMOS here for example (where 'a' is the input): http://en.wikipedia.org/wiki/Inverter_%28logic_gate%29.
To get an idea of one problem with NMOS that CMOS solves, consider the inverter example when the input is high. In that case, you get a continuous current from the power source to ground, meaning you're drawing power (and generating heat) even in the steady (static) state. CMOS on the other hand is designed to only draw power while the circuit is switching. Studying the circuit on the wiki article might give some rough idea of how that works.
The basic logic elements tend to be more involved in CMOS, which makes use of symmetrical pairs of transistors with different doping. (Roughly, the doping determines whether a high or a low voltage "closes" the transistor.) Compare the implementation of a NOT gate for NMOS and CMOS here for example (where 'a' is the input): http://en.wikipedia.org/wiki/Inverter_%28logic_gate%29.
To get an idea of one problem with NMOS that CMOS solves, consider the inverter example when the input is high. In that case, you get a continuous current from the power source to ground, meaning you're drawing power (and generating heat) even in the steady (static) state. CMOS on the other hand is designed to only draw power while the circuit is switching. Studying the circuit on the wiki article might give some rough idea of how that works.