As this was long overdue, I decided to make a head unit install DIY for the 03-04 Civic. This may apply to other years as well, but AFAIK, it is only for the 03-04. This DIY was created using an 04 LX coupe.
NOTE: The first 3 pictures are for an install on an auto, the following 4 will be for an install on a 5 speed. After the first 3 steps for each, there are no differences.
1) Stick your hand under the trim ring and pull
2) The ring comes off easily
3) Stick your finger in the location shown and pull up HARD. It can be very stiff but it does come out. There is a hole there to stick your finger in and make it easier.
4) The console piece does come off but it can be a pain in the ass sometimes. If it seems stuck in one part, look very closely to where the clip is (the console piece will be cut out a little just above it), stick a very small screwdriver and try to push the clip out. It will come out eventually so be persistent.
NOTE: The following 3 steps are for an install on a 5 speed. Following these steps, starting at number one again are instructions that apply to both manual and auto.
1) This is what the 5 speed center console looks like
2) Pull up on the shifter console area like how I am in the picture. You want to pull from inside the shiftboot area. You may want to pull with both hands. One hand on the left side, and one on the right side. Its easier if you do it with both. The only reason I have one hand in the pic, is the simple fact I used the other to take the pic. After you pull the left and right sides up, the front and back should just come off. There is nothing but clips holding this area down.
3) You should be able to turn the area around the shifter sideways. Once this is done, you can follow the steps from the DIY for the auto, its exactly the same. As you can see in the pic, its not necessary to take off the shift knob.
NOTE: The remaining steps apply to both manual and automatic vehicles
1) Use a phillips head screwdriver to remove the 2 screws located near the cup holders on either side of the console
2) Stick your hand under the "horseshoe shaped piece" as shown and pull it out. It is simply held in by clips, 2 on each side. Pull the sides out first and then pull the entire piece out by pulling up and back. Unplug the cigarette lighter and set this piece aside.
3) This is what your dash should now look like, and you can start taking the head unit out.
4) Remove these 2 screws to allow you to take the panel containing your HVAC controls, hazard light and head unit to come out. You can use either a very short phillips head screwdriver or an 8mm socket and ratchet. I highly recommend the ratchet. One screw is in the center and one is towards the right, but they are up underneath the dash and you may have to get under there at a wierd angle to see them, but they are very easy to get out using a ratchet.
5) Stick your hand behind the metal bar that you just took the screws out of and push it kind of up and forward. The top of this bar is part of the panel containing the head unit and the bottom half is part of the car. Push on the bar so that the head unit pops out. It may be stiff if it hasn't been removed before but it does come out.
That's all there is to it, and reassembly is the exact opposite of disassembly.
If you get stuck, please feel free to post any questions in this thread.