For your children: encourage "show and tell" by asking children to introduce their new presents to family members. Use questions to develop a framework and help them to expand on the information they are giving. This is a great way to get your children making presentations because their enthusiasm over-rides any fear.
For adults: try a "present debate" in which everyone has to give a one minute speech arguing why they have received the ultimate present. After each round, vote for the most popular gift based on the persuasive speech (not your own preferences!) Winner avoids the washing up.
Effective public speaking begins with a basic interest in the subject and a desire to communicate. Both of these criteria are answered as you unwrap a fabulous Christmas present and can't wait to tell everyone about it!