Both the Catholic and Orthodox Churches have many traditions and customs surrounding the Feast of the Assumption of the Blessed Virgin Mary, body and soul into heaven. The domestic church, that is to say the family, like the Holy Family of Jesus, Mary and Joseph practices its Christian faith in such ways as to continuously deepen their belief in their holy religion. As a family there are many traditions at their disposal, if they so desire to follow them. Obviously the recitation of the rosary as a family would be a wholesome start. Years ago, we would pray the rosary along with the Pope John Paul II via a cassette tape. Then there would be the saying of a novena in preparation of this feast.
The Catholic Church has always professed her belief that Mary was assumed body and soul into heaven by a unique privilege from God. In 1950, Pope Pius XII defined the dogma of the Assumption of Mary into heaven, without touching the question as to whether Mary actually died or not. This ecclesiastical event, provoked a new Mass to be written up in the Roman Rite (Signum Magmum) for the feast. In the Ambroisan Rite of Milan the traditional liturgical color of black for this feast was changed to white (or gold).
Today there are over 30 countries in which hold this feast (August 15) as a public holiday. Mother's day is observed on this day in Costa Rica and Belgium. The Armenian Church blesses grapes on this feast. In the Roman Ritual, there is a blessing for fruits and herbs which is reserved explicitly for the Feast of the Assumption. In many localities of Europe, families bring fruit to their local parishes to be blessed by the pastor. Others celebrate this day by joining into various procession held in Mary's honor.
In Austria and France priests still preform the "Blessing of the Alps", Not only are the mountains blessed, but also meadows and farms. In some places, the "Blessing of the Sea" is done today, such as in some ports in Italy and Portugal. Finally, there are several traditional food stuffs that are served in families on this day around the world. See Wikipedia's article on the Assumption of Mary.
As I have already mentioned above, Pope Pius XII introduced a new Mass of the Assumption when it was proclaimed a doctrine of the Catholic Church. The domestic church as a family listen to the Propers of the Mass Signum Magnum on YouTube on the glorious Feast of Mary's Assumption: Assumption 15th August (Fontgombault Abbey)
Armenians, the faithful bring the first grapes from their vineyards to church on Assumption Day to have them solemnly blessed by the priest. Before breakfast the father distributes them to his family. No one would dream of tasting the new harvest before consuming the first blessed grapes on Our Lady's Day.
In Sicily people keep a partial or total abstinence from fruit during the first two weeks of August (La Quindicina) in honor of the Blessed Virgin. On the feast day itself they have all kinds of fruit blessed in church and serve them at dinner. They also present each other with baskets of fruit on Assumption Day.
From early centuries the Feast of the Assumption was a day of great religious processions. This popular custom seems to have started with the ancient Roman practice, which Pope Sergius I (701) inaugurated, of having liturgical prayer-processions (litaniae) on the major feasts of Mary. In many places of central Europe, also in Spain, France, Italy, and South America, such processions are held. In Austria the faithful, led by the priest, walk through the fields and meadows imploring God's blessing upon the harvest with prayer and hymns. - Catholic Activity: Assumption Day