Kallmann Syndrome is diagnosed by two key symptoms: absent puberty and lack of a sense of smell.
Pubescent development is evaluated by a physical exam. Other tests will be run such as blood work (to find out the levels of LH, FSH, and primary sex hormone), a hand x-ray (to determine bone age), and possibly a CT scan (in order to rule out other problems with the pituitary gland.)
Typically, a doctor only needs to ask a patient if they can smell. However, I have heard of one doctor "proving it" by putting wet coffee grounds in a bag and asking the patient to smell the bag and tell him what is inside.