Be simple and direct, but not overly technical. Alzheimer’s is a big word that may not mean much to kids of any age, and “disease” can sound like something catching.
So simplify: “Grandma has a memory problem.” Or, “Grandma has a disease that is sort of like if you had a tape recorder in your head, but the tape recorder is turned off. When she was younger, the tape recorder was on, so she remembers a lot of things from her past, but she can’t remember recent things as well.”
Put the disease in perspective for a younger child. Ask, “Are you really good at everything? Well, sometimes people aren’t very good at memory.” Explain that lots of people have problems when they get older — sometimes you need glasses, sometimes a cane or a walker. Sometimes you can’t remember. It doesn’t mean you can’t do anything anymore. Explain what sorts of things the person can still do (play cards, take walks, give hugs, and so on).
Assure teenagers, who have a longer history of life with that person, that behavioral issues (like aggression) or memory changes (like forgetting the teen’s name) are effects of the disease and shouldn’t be taken personally.