Our dishwasher just started overflowing into the sink and the counter tops through the thing on top that I think is called an air gap. What would be causing this all of a sudden? We have had the dishwasher for 9 years and haven't changed anything. How can I fix it?

Joni

If your sink is draining OK then the hose from the air gap has become clogged.
If you have a disposal this hose will be connected to the disposal.
If you have a disposal first check that there is no waste food in it.
Remove the hose from the sink drain or the disposal by loosening the clamp on it.
Clear hose with a wire coat hanger.

Yep, Harold is right. Air gaps don't fail but the line to the sink trap can get plugged with food and junk. Might be too long for a coat hanger so a 1/4" snake may come in handy.