DeathRay: the impedance of a capacitor (Xc) is determined by:
Xc = 1/(2(pi)FC)
where F is the applied frequency and C is the capacitance in Farads. It's common practice to put a rather small (say 1uF) capacitor directly across 120VAC power lines coming into a power supply; your computer PSU probably has one. At 60Hz AC, the impedance is quite high (2.6Kohms). However, at high frequencies, the impedance is much lower. Let's say your computer PSU, which is a switching power supply, switches at 100KHz. The capacitor presents an impedance of 1.6ohms at that frequency. So, it will help to filter out the 100KHz switching noise but will not affect the 60Hz AC signal.
For power factor correction, all you need to know is the above formula for the reactance (imaginary component of impedance) of the capacitor and the power factor of your AC motor. If you AC motor is a 1000W motor with a power factor of 0.85, then (1-0.85)*1000 is the reactive component of the motor, 150W. Convert that to ohms using P^2 = V^2/R to get a reactance of 1.56ohms.
Most AC motors have an inductive-type reactance, which is the opposite of capacitive reactance. So, you can cancel it out by applying a capacitor with the same reactance as the AC motor - 1.56 ohms. In this case, by manipulating the formula for capacitive reactance, C = 1/(2(pi)FXc), where F is again 60Hz and Xc is 1.56 ohms. That gives you a capacitance of 1700uF. So, you can restore unity power factor by applying a 1700uF capacitor in parallel with your motor.
Anyway, DON'T TRY THIS AT HOME unless you know what you're doing. The capacitor must be rated for 120VAC or higher, for starters.
Another way to think of it is to remember that capacitors resist changes in voltage while inductors resist changes in current. As the voltage on your AC sine wave ramps up, a capacitor will draw current to charge to that voltage - it is resisting the increasing voltage. Then, as the voltage ramps down, the capacitor supplies extra current to discharge to the AC voltage. So, it will sit there and absorb current and push it back every cycle. An inductor does the opposite, pushing current to the line as the voltage increases and pulling current from the line as the voltage decreases.
So, the problem with low power factor in typical household motors is that there is all this extra current being pushed back and forth from the motor inductors without actually doing anything useful. It simply gets dissipated in the wiring resistance and lowers the amount of power the electrical grid can supply. By adding power factor correction capacitors, instead of all the current being pushed and pulled to and from the generating station, it is pushed into and pulled out of the capacitor instead, reducing the amount of current drawn through the power lines.