Here's the procedure from the manual with some diagrams that might help
Document ID# 765021
2002 Chevrolet Corvette
Transmission Fluid Replacement
1. Raise and suitably support the vehicle; ensure that the vehicle is level. Refer to Lifting and Jacking the Vehicle in General Information.
2. Clean away all dirt and debris from the transmission fluid drain plug area.
3. Remove the drain plug.
4. Allow the system to drain.
Use the correct fastener in the correct location. Replacement fasteners must be the correct part number for that application. Fasteners requiring replacement or fasteners requiring the use of thread locking compound or sealant are identified in the service procedure. Do not use paints, lubricants, or corrosion inhibitors on fasteners or fastener joint surfaces unless specified. These coatings affect fastener torque and joint clamping force and may damage the fastener. Use the correct tightening sequence and specifications when installing fasteners in order to avoid damage to parts and systems.
1. Install the transmission fluid drain plug.
Tighten the transmission fluid drain plug to 27 N•m (20 lb ft).
2. Clean away all dirt and debris from the transmission fluid fill plug area.
3. Remove the fill plug.
4. Fill the transmission with DEXRON®-III transmission fluid, until even with the bottom of the fill plug hole.
5. Install the transmission fluid fill plug.
Tighten the transmission fluid fill plug to 27 N•m (20 lb ft).
6. Lower the vehicle.