How can I help stimulate someone's brain with dementia?

Depends on a stage. Depends on a stage. Some activities include puzzles (if not too frustrating), some exercises about meaning of words and basic things (with more advanced stages); reminiscing, etc. If a person is in a skilled nursing facility, they have day programming dedicated to that. If a person, still lives at home and dementia is mild, then probably adult day health care centers in your area might help.