Alzheimer's Disease is a neurocognitive disorder. It is one of many different types of dementia and is described in the APA's Diagnostic and Statical Manual of Mental Disorders.
Specific criteria are required for either a probable or possible diagnosis. A probable diagnosis includes family history of the disease, plus clear evidence of loss of memory, steadily progressive, gradual decline in cognition without extended plateaus, and no evidence of other contributing factors (e.g., infections or other mental disorders). A possible diagnosis is made if the above is present without family history.
The following link is to the Alzheimer's Association's website and lists 10 early warning signs and symptoms: http://www.alz.org/alzheimers_disease_10_signs_of_alzheimers.asp
A diagnosis of Alzheimer's should only be made by a physician. Other conditions, such as a urinary tract infecton, can mimic dementia if left untreated.