How does a young man tell his family of his desire to marry when he is shy?

Informing one's family about marriage is not a condition for its validity. Therefore, a mature, sane adult may marry without their parents' knowledge. The presence of a guardian for the woman is a pillar of the marriage contract only. If you wish to inform your family, you can do so via a message or a phone call, or through another person if you feel shy. You must overcome shyness that prevents marriage, because it is blameworthy shyness if it prevents one from doing good.