How does one go about getting a diagnosis of dementia?

Go to a neurologist and have them do a short cognitive evaluation called the MME. It's a series of question, iirc about 12. If there is indication of impairment the neurologist will likely order a neuro-psych evaluation or you could ask for that evaluation.

The neuro psych evaluation is much more in depth, can not be fooled and takes about 5-6 hours. It can be done over two days.

Have a neurologist do an examination.

I took my mother in law to a free clinic and asked them to do a cognitive function test. She failed, and they did follow-up testing. She still needs a brain scan to diagnose the specific type of dementia, but has been diagnosed with "unspecified dementia" as of now.