Loosen the bleeder screw then squeeze the piston with a large channel lock pliers or C-clamp. I have a 96 Grand Prix SE and had the same problem....has to be screwed in not pushed in. Take the calipers off & take them to Auto Zone - they will do it for free.
Disk brakes by design do not have adjustments - the pads 'float' with the caliper and the piston movement.
be sure to purcahse the tool to "screw" the caliper piston in. If you try to push the piston in on rear disc brakes you will damange the caliper.
I have used a large "C" clamp, to compress the caliper flush to the face.
Disc, front and rear.
You will need a 3/8" allen wrench to remove the anchor pins for the calipers and a "C" clamp to compress the piston back into the caliper.
Warped front rotors are the most likely cause
If you front brakes rattle, it is usually caused by a a stuck puck or piston in your brake assembly. When this happens, the piston does not fully retract at times causing you brake pad or pads to wear excessibly and when the piston finally retracts fully and does not keep constant pressure on your pads you get a rattle. I had this problem on my F-150 and the brake guy solved this by installing steel pucks and lube.
A 1996 camaro has the same DISK brakes as a 2001. It does not have drum brakes.
Master cylinder
like disk brakes
drum brakes on rear of 1996 ford not disk
All you need to do is remove one long troq srew at the top of the brake assembly, and the whole thing will swing down pop the old pads out, compress the piston and pop the new ones in and just slide the whole thing back together. After a few times it only takes about 5 minutes, including taking the tire off.