It this way, new elements where incorporated in the altar which is put together for the deceased, like candles, chopped paper, bread, candy skulls and incense, as well as pictures of the deceased whom the ritual is dedicated to.
The altar is a fundamental piece of the ritual which is done on "Dia de Muertos" given that it works as a symbolic representation of the vision we have about death.
The key things it should have are the following:
Candles.- It's function is to light the path for those who have passed away, they tend to be purple and white to represent grief and the purity of the soul.
Marigold flowers (Flor de cempasúchil).- their shape and color evokes the sun, the star which in Aztec tradition guided the souls of the dead.
Pan de Muerto (Bread of the Dead).- It is a round pastry with bone shapes on top making a cross, they are sprinkled with sugar, it is a representation of Eucharist, consecration of the bread in the body of Christ.
Food.- They offer the foods that those who passed away enjoyed when they were alive. The dead do not consume the food, but it is said that they take the essence of the dish, and that if you try the food you'll notice that it lost it's flavor completely.
Skulls.- they can be made of either sugar or clay, and they are a reference to death itself, as a reminder that it is always present.
Water.- it signifies the purity of the soul, the custom is to put a jug of water on the alter, given that it is believed that the dead go a long way before reaching the place where they belong and they might get thirsty on the way.
Salt.- it is used to prevent impure souls from reaching the altar
Dog.- A Xoloitzcuintle dog is used to represent the god Xolotl, and it is placed because of the belief that it will guide the deceased to find their way.
Rug.- it is placed to offer them a space to rest before they embark in their journey back to the great beyond.
Another tradition on "Dia de Muertos" are the famous "Calaveritas" (literary epitaphs) with the intention of being funny, they are a rhyme made about people who are still alive and tell the story of how Death comes for them.