One who merely contemplates the Hagada does not fulfill the obligation to tell the Exodus story, as it is stated, “Tell your child” (Shemot 13:8), i.e., express the story verbally. However, it is not necessary for all participants to recite the Hagada; the main thing is that the Seder leader or someone else recites it aloud, and the others hear it. Indeed, it was customary for the oldest participant to read and explain the Hagada while everyone else listened. This is, in fact, the way stories are usually told (see Pesaḥim 116b).
In order to include everyone in the recitation of the Hagada, it is customary nowadays for the Seder leader to read it aloud while everyone else quietly reads along with him. Others have participants take turns reading paragraphs from the Hagada, but only a reader who is a bar or bat mitzva can fulfill this obligation on behalf of others.
When several sets of parents and children have the Seder together, it is not necessary for each parent to tell the story to his child separately; it is sufficient for the Seder leader or another participant to read the Hagada aloud, because as long as the parent makes sure that his child participates in the Seder and hears the story, he has fulfilled the mitzva to “tell your child.” One who wishes to enhance the mitzva can further explain the Exodus to his child during the meal.
In order to fulfill the mitzva of telling the Exodus story, one must at the very least explain or hear an explanation of the Paschal sacrifice, matza, and maror. This makes clear that we were slaves in Egypt and that God redeemed us. Therefore, parents who see that their children are falling asleep must tell them about the korban Pesaḥ, matza, and maror, and explain their meaning. The same principle applies to a participant who is unable to complete the Hagada due to illness or military duty (see above 15:9).