How can I get my mother evaluated for Alzheimer's disease and dementia?

Take her to a gerontologist. They specialize in the health issues of the elderly.

With how insurance works in the US, if you are in the US, take her to her primary who will do a basic evaluation(clock test, describe a scene) and if she doesn't pass they will refer you to a neurologist/psychiatrist for further evaluation. Ideally that will be someone that specializes with the elderly but in my experience they are hard to find. Where I live, we only have 2 available for a population of a million people. It literally took months to get the first appt and even for an urgent appt it can take weeks.