How does a doctor test for ADHD on older adults?

ADD is testable . We look for symptoms & signs consistent with add. These include disorganization, poor interpersonal relationships, financial mismanagement, procrastination, disrupted executive cortical management, poor attention, impulsivity, interpersonal relationship problems, drug abuse, poor employment performance; among many others. We test for these signs in the exam.
No specific tests. To diagnose adhd in adults a health care provider takes a detailed history about the patient's childhood development, school performance, social abilities, and job performance. There are also a number of pen and paper tests that screen for adhd in adults. More expensive evaluations are also available at specialty clinics.
Psychiatry. The evaluation for adhd is very involved. It involves questionnaires (connor, burke), IQ testing, psychological evaluation to rule out mood disorders/personality disorders, medical screening for vitamin deficiencies, thyroid disorders, etc. You would best be served by seeing a general practitioner to rule out medical issues and then an evaluation with a psychiatrist would be helpful.