Lowering an '84-'87 Civic/CRX (with stock motor and suspension):
The front is really easy, you don't even need to jack up the car if you know where the adjustment nut is! If you only need about an inch, just loosen the height adjustment nut. Doing this brought the height of my '86 CRX from about 24" to 22 and 7/8". Before you take any measurements roll the car back and forth and bounce it to settle the suspension. Measure squarely through the center of the wheel to the lower edge of the wheel well. Make sure that the car is on a flat surface with properly inflated tires and a full gas tank.
I would not recommend going any lower than about an inch at the front without taking out the torsion springs. 1 and 1/8" was as far as I could go and still have enough threads left on the adjustment nut to feel safe.
To lower the car more than an inch at the front you will need to remove the torsion springs. To do this you will need to set the front of the car on jack stands and place a jack under the spindle of the side you are working on. Then remove the metal dust cap at the rear and the rubber cap from the front of the torsion springs. Remove the rear spring clip, then using a heavy hammer and a large heavy punch or heavy round rod (I use a lug wrench with the bent end cut off), pound the torsion bars forward about 3/4" and remove the front spring clip. Then spray the splines with lubricant and pound the springs back untill they fall out. You may need to adjust the height if the jack untill you relieve the tension on the spring.
Next you will need to grind one spline off of the rear of the torsion spring next to the spline key. Grind the spline to the right of the key on the passenger side and to the left of the key for the drivers side then lube up the splines and install them in the reverse order from which you took them out. You may need to adjust the height of the jack in order to get the splines to align. Make sure that they go in one spline off from their stock location.
Tighten the height adjustment nut all the way! Once you get the car on the ground loosen the nut untill you get the desired height.
You can grind 2 or 3 splines if you are truly insane!
No matter how far you lower your car, it is a good idea to have the front end aligned when you are done. If you need a little more camber you can elongate the strut mounting holes toward the inside of the car, and if you need a little more caster you can pull the crossmember forward. Also, swapping in the lower arms from an '86-'89 Integra will give you about 1 degree of negative camber.
You should also consider replacing your struts with something adjustable like Tokico Illuminas, especially if you are planning to go really low.
At the rear you can just cut the springs or use aftermarket springs. You won't even need a spring compressor to remove them. If you go with the cutting method, one coil will usually give you about 1' drop, but do some trial and error before you start cutting too much off your coils since you can't add the coils back on. I've also heard that you can use Civic wagon springs in the back for about 1' drop, but I have not verified this. I have been using Tokico progressive springs. Tokico says that these springs will lower your car between 1"-1.5", but they really only lower it about .5", so I just cut the springs with a cut off wheel until I got the desired ride height. You can also get progressive springs from Eibach and adjustable springs from Ground Control.
You will need to find an adjustable panhard bar if you go any lower than about 1"-1.5" at the rear, or you can cut and weld yours to the appropriate length.
Note:
You can heat the rear springs with a torch and just let the car drop but the car will handle poorly, I wouldn't recommend it!