Not easy. Clinically, alzheimer's tends to be a smooth decline over time, while vascular dementia declines in steps, as small regions of the brain lose function. Neuropsychological testing may lend evidence for, but not prove, one cause or the other. A definitive diagnosis can only be made by brain biopsy (which is rarely done), or at autopsy.
PET scan. There is no easy way to distinguish but a pet scan can be helpful to make a diagnosis.