I successfully did this on my 2001 Honda Civic.
You have to remove the entire center console to get to the light. I recommend actually having the replacement bulb prior to starting. I used a Sylvania 74 that I picked up at the local auto parts store. They are tiny bulbs. About $3.
Here is a diagram I found that was very helpful in removing the center console:

In picture B you will see that there are two screws hidden underneath the part you just removed. You need to remove those two screws plus the two tabs shown in front and the two screws located in the rear close to the floor.
You will need to put the shift into neutral or farther back to then lift out the entire console.
Once the console is removed you will see a wire going into the right side just underneath the gear shift. If you look into where it's going, you will see the back side of a small round socket. Rotate the socket about 90 degrees and it should come out. Voila! The bulb.
Simply pull the bulb out and push in a new one. Turn on the headlights to test. The bulb should be nicely lit.
Now push the socket back into where it came from and rotate back 90 degrees to lock it in place. If you reverse the rest of the instructions, putting the console back together will just take a minute or two.
Finally, write an email to Honda and tell them what you think about how easy it is to replace this lamp.