From the CorvetteForum:

Turn on the headlights and back off one position to kill the lights.

Unscrew the 3 small screws on the black plastic housing around the
headlight. Gently pull the housing clear.

Reach down around the headlight unit and release the bulb holder. It
unscrews counter clockwise but it has a plastic clip which you need to
squeeze to release it.

Change the bulb. Reseat the bulb holder and turn until it clicks back in place.

Put the plastic housing back in place making sure to locate the small
plastic tab in the bracket on the headlamp cover. Replace the 3 screws
and close the lights.

10 minute job.

3057 bulb works.

An alternate way, if you have small hands:

Push your fingers into the air vent below the light.  Push it back and
out of the way.

Turn your hand upward and remove the socket as described above and pull
it out of the air vent.

Change the bulb and reverse the process to assemble.

For either way, do not touch the bulb with your bar hand/fingers.  Wear
surgical gloves or something similar.  The oil from your hands will
shorten bulb life.

On my C5 it's easy. You just rotate/push the assembly upward from the
outside and prop it open with something (I use the top of a water bottle)
while you change the bulb.

Actually the manual, starting in section 8-156 through 8-160 (98), gives
very detailed description and pictures to remove/replace the turn signal
bulb. The brake duct that needs moved is not screwed or latched fast, just
some easy detents to pop loose if you come in from the bottom, recommended.