I asked my husband he is a Santa Muertero and Tata Nganga in Palo Mayombe and he says anything connected with death and the death energy which could include pictures of your dead ancestors and some of their personal belongings including in the case of cremation the ancestors themselves.
An image or statue of Santa Muerte. Underneath the state/image should be a wooden box preferably one that can be locked. Inside of this wrapped in a purple cloth and tied with a black ribbon should be quartz crystals, magnets, bones of nocturnal animals, human remains, and dirt tooken from the cemetery. This box along with your statue or image is the heart of your altar. He says you don't have to have all of these things but that is what they do in Mexico to make there magic real strong.
For offerings she likes Tequila, Mezcal, Whiskey, Cigars, Cigarettes, Conchas, Cocaine, Cool Water, Marijuana, Black Coffee, Fruits, (especially apples) red roses, thick bread, chocolates, incense, money, jewelry, candles, candies or you could even hire someone or a band to sing sonnets to her.
Give her, her own space no matter how small it is. She doesn't like to be around other saints and will become very jealous of them. Remove anything from her altar as soon as it starts to show signs of spoil. Throw these items in the trash or take them to a cemetery and leave them underneath a shady tree. Always keep any promises you make to her. For smokes you can leave them on her altar for a day and then blow the smoke on her image while praying to her. And remember Santa Muerte is not like other saints she doesn't judge. She'll help a killer just as quick as she'll help a cop just as long as shes treated right by the devotee and provided with the appropriate offerings. If you have any questions please feel free to ask he likes clarifying misconceptions involving her because there are alot of them out there.