Generally speaking, you want reduce the amount of restriction to allow the engine to suck in as much air as it needs to. Simply removing the silencer from the front of the airbox will help. This will also allow more engine sound to be heard, especially a bug sucking sound (if you try it, you'll know what I mean). I heard someone refer to it as a big Hoover sound.
From there you can add a K&N high flow air filter. It's available most auto parts stores and should cost somewhere around $50-$60. It's a special filter that is designed to allow more air the regular paper filters through. It also is designed to be reusable--you can clean it and put it back in your car--saves money and resources in the long run. Actual gains are arguable from a few horsepower to nothing. You be the judge.
You also can run some additional hose for a "cold air" intake system. I did this on my TC. I removed the silencer tube first. Then I bought some clear jacuzzi water hose (3" outer diameter) about 3.5 feet. I inserted one end into the hole in the airbox where the silencer was and ran the other end down, behind the headlight, to the black rectangular cutouts under the painted part of the bumper. The air at this area of the engine compartment has not been heated up by the engine--it is still "cold" air from the outside. The colder the air coming into the engine, the smoother it will run. You car runs great on a cool summer night, doesn't it?
Additionally, I turned the hose into the outer rectangular hole. When you're going down the road, air will be forced into the tube, thus delivering more air then the engine would need. This forced air setup is called "ram air". You may have heard of it on Pontiac Firebirds, it's a popular sales catch phrase.
PVC pipe is also common for this type of air intake setup. Any hose that won't get too heated up is a good choice. My jacuzzi hose probably isn't the best--I'll be redoing it when I've researched some other options.
Drop me a note if you have any suggestions or your experiences with your own car.