How firmly you hold the disc will vary depending on the grip, but in most cases you want a firm grip as opposed to a loose grip. A firm grip will result in better control, more spin, more power and a better flight with greater distance and accuracy.
There’s definitely a balance to grip pressure though, and the best way to figure it out is with experience, but the most important tips I can give you are:
Don’t hold onto the disc so tightly that your fingers hurt.
Don’t hold onto the disc so loosely that it could be swatted from you grip by someone walking by.