Common Day of the Dead traditions include creating altars to honor the dead, laying out offerings, sharing stories of the deceased, as well as cleaning and decorating gravesites. Because Day of the Dead is a very festive, creative holiday, current Day of the Dead customs also include festivals, parades, and the making of Dia de los Muertos crafts. 
The key purpose behind these Day of the Dead customs is to make contact with the spirits of the dead, to let them know that they are not forgotten and that their loved ones on earth still care about them. It is a way of keeping the connection between loved ones alive, though they may be physically separated by death.