You could buy a kit like this one.
Cabela's Livewell Aerating Kit
I had talked to someone who had built one. He had an extra bilge pump, and coleman cooler. He then mounted the pump in the bottom corner with small screws, and sealed the screws from leaks. Then ran flexible hard plastic tube from the pump straight up to about 1/2 inch from the top, so you can close the lid. And mounted it up there with clamps and screws. Then he put small holes in the tube, so it made sort of a current. He then cut out a small notch so the pump wire would come out of the cooler and still close the lid. He then plugged up any gaps where the wire exits. I heard it works well.