First off ~ Welcome
lilc2197 to the Corvette Action Center Community ~
Throwout bearing, you must have a 4-speed
Throwout bearings have been known to "squeel" a bit from time to time, sometimes even newly replaced ones
When the squeel starts, try pushing in on the clutch, or put pressure on the clutch and see if the squeeling stops. My guess is your dad is probably right about the throw out bearing being noisy.
To put a new one in isn't real hard, but it will seem that way to you with you experience..
I don't know if there is a "how to" for changing out the bearing, but you'll need to disconnect the shifter linkage, then disconnect the drive shaft (which will cause fluid to come out of the tailshaft of the transmission), then remove the transmission (4 bolts) pull the transmission back away from the bell housing, then remove the splash pan on the bell housing (that's easier than removing the bell housing, which you can do if you want, it just has a lot more bolts to remove).
The Bearing sits in a shaft that looks like a Fork pay attention to how it is installed because the new has to go back in the same way the old one was installed.. As Long as you leave the Clutch and Clutch Plate in place, you shouldn't have to use a "pilot" shaft for alignment before putting it all back together, then just reverse the removal prossess to put everything back together.
You'll need to have the car up on Jack Stands or a hoist, BE VERY SURE IT IS SECURELY ON THE JACK STANDS
BEFORE YOU CRAWL UNDER THE CAR Safty First, SAFETY FIRST..
This is short version, but it will give you an idea of what your looking forward too.. It really isn't to difficult and it is a nice starter project
You'll get a bit greasy, but your 76 will love having YOU working on her
Bud