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You tie the filter down with plastic zip ties and eliminate the cover for the airbox altogether. A more permanent tasteful change is to a Z06 airbox. Some guy who went supercharger gave me his, and I left it on the car like that. It doesn't change the performance, but may let the filter wear a bit more evenly. Or you could cut the opening to your existing cover. The cover helps seal the thing filter to the intake. I wouldn't ditch it for zipties.
There are kind of two methods. One is like BRISLS1 stated. You simply remove half of the air box and zip tie the filter in place in the remaining half.
The second one is a Flip tie. You remove half of the air box, turn the other half over so it faces the radiator shroud, cut a hole in the shroud, and then zip tie the filter into the inverted "flipped" half. See the link: http://forums.corvetteforum.com/c5-g...-write-up.html