Removing the airbox
Note: This article is undergoing a major revision, and we don't have good documentation on either process. You'll be on your own a little bit, but with a good amount of patience you should be able to figure it out.
The old airbox removal article suggested that you would have to break your airbox to get it out. This is not true. You should be able to remove it undamaged if you are patient and careful enough. It shouldn't be necessary to rip it into pieces in order to remove it.
Removal from the side
To get started, you need to remove a lot of pieces from the bike. Follow the directions for removing the carbs, including removing the carbs.
Before:
If you're going to take the airbox out altogether, it should be for good. You need to remove the 10 screws that hold the two halves of the box together. Remove the battery, and the two bolts that hold the back of the box to the frame under the battery, then start to work on those screws. When you've got them all out, you should be able to break the two halves apart (if you have trouble doing this, then you missed a screw; they're hidden all over the perimeter of the box).
Remove the plastics and filter element from inside the box at this time, then work the left half of the box out of the frame, then the right.
It is possible to do this carefully and not damage the box. The problem is that the box is bigger than the frame space it occupies, and is tricky to work out. This is a frustrating job, and can require a lot of grunt work. You can make the job a little easier by removing the two bolts at the inside front of the rear fender and pulling the fender back a bit. This owner managed to get his out with only two broken pieces.
But with no airbox in the way and the modular filter pods in their place, removing the carbs is as easy as loosening a few intake screws and popping them out. This is good, because removing the airbox is going to force you to remove the carbs pretty often in order to get the jetting right. If you're a new rider, it is not recommended that you mess with the intake system. Go out and ride.
Removal from the rear
One of our owners has reported that he had good luck removing the airbox from the rear of the bike. Remove the rear wheel, both rear under-fender pieces, and the side fairings. Then, disconnect the airbox from the carbs and pull it all the way out through the back. You can get the airbox out intact this way.