Cruzer82,
Raise the RF of the car (use a jack stand). You can lay under the car and see the a/c condensate drain protruding from a plastic nipple on the firewall, at the rear of the right engine head.
Use a small "tack puller" type screwdriver and remove the rubber 90 degree elbow that is attached to the plastic nipple. It is about 3/8 or 1/2 inch in diameter.
Clean out the rubber elbow and cut off the moulded end. It is moulded into the shape of a "split pea" and is prone to clogging and doesn't drain fast enough during hot, humid weather.
You can use a plastic zip-tie to push inside the plastic nipple to clear any debris (use the non-clasp end).
Coat the inside of the rubber elbow (at the nipple end) with a slight amount of silicone dielectric grease, to help the elbow slide on the nipple.
This must be done while the engine is cold because your hand will be touching the exhaust manifold and engine head.
Good luck - my 1999 C5 was immobilized for five days while I was out-of-state, on vacation. A clogged drain caused water to spill into the passenger compartment and ruin the computer located in the passenger footwell.
This is a common problem and one that was ignored by Chevrolet on the C5.