When I was a Public Health Nurse and also worked in schools, I followed a number of kids with either FASD or prenatal drug exposure related problems.
Theses are both things that there is not a specific test for, so there is no way to tell for sure. With conditions like that, the diagnosis is made on the basis of symptoms (things like like hyperactivity, emotional regulation difficulties, behaviors) that were mentioned by the other posters and physical findings ( the things about the body that are visible, like the low set ears, small stature, small face). For each syndrome, there is a long list of the known symptoms and findings. To make a diagnosis, the signs and symptoms the person has ate 'ticked off' against the complete list. Each dignosis has a specific number of signs and symptoms that must be present to make the diagnosis. There may be certain symptoms or findings that 'must' be present to make the diagnosis -those are usually the things that are so common to that syndrome that all known cases have them, or they are only seen in that syndrome and not in any others. Many syndromes share symptoms and, as more us known, the symptoms needed to 'fit' that diagnosis may change. That happened with autism, where the diagnosis changed and included people who were not previously included in that diagnosis.
There are also syndromes - like Down Syndrome - that were initially made only on signs and symptom, but also include genetic testing since that has been available.