TOS is often diagnosed after excluding other conditions that may be present with similar symptoms, such as musculoskeletal injuries of the cervical spine, shoulder girdle or arm, cervical radiculopathy or upper nerve entrapment, idiopathic inflammation of the brachial plexus (aka Parsonage-Turner syndrome), and brachial plexus compression due to an infiltrative process or space-occupying mass (e.g. Pancoast tumor of the lung apex) . An ulnar nerve entrapment at the elbow or a carpal tunnel entrapment at the wrist, can also cause the TOS symptoms. 
However there are some provocative tests that can help diagnose the TOS.
People suffering from TOS often slouch their shoulders, giving them a drooped appearance. The slouching can compress the nerves and arteries near the thoracic outlet. Being overweight can cause problems with posture, and women who have very large breast may also have a droopy posture. TOS affects three times more women than men .
Palpation of the brachial plexus, the scalene muscles, the trapezius muscles, or the anterior chest wall may reveal tenderness. 
The tests that can make a clearer diagnose of a TOS include the EAST or Roos test, the Adson test, the Wright test and the costoclavicular test. 
In the EAST or Roos test the patient places both shoulders in a 90 degrees abduction and external rotation, and then opens and closes the hands slowly for three minutes. This will constrict the costoclavicular space. The test is positive if the symptoms are reproduced and the patient cannot sustain this test the whole tree minutes. 
In the Adson test the patient extends the neck and rotates the head towards the involved extremity, which is held at the side. This will constrict the interscalene triangle. The patient is asked to take a deep breath and hold it while the physical therapist checks the patient’s radial pulse. The test is considered positive if a change in a radial pulse is detected. 
The Wright test is similar to the EAST or Roots test, but the patient is not asked to open and close both hands. Instead, the radial pulse is checked. Once again, if the physical therapist detects any changes in the radial pulse, or if the symptoms are reproduced, the test is positive.
In the costoclavicular test or Eden's test, the physical therapist depresses the patient’s shoulder, which will constrict the costoclavicular space and creates tension across the pectoralis minor. The test is positive if the symptoms are elicited. 
Stress avoidance, work simplification and job site modification are recommended to avoid sustained muscle contracture and repetitive or overhead work that worsens the symptoms.
Physical therapy, through a passive mobilization of the neck, of the cervical spine vertebras, of the collar bone and of the first rib, will reduce the muscle tension and the pressure of the collar bone and the first rib. Stretching of the scalene muscles will also help to lower the pressure on the blood vessels and the nerves.
Postural exercises can also be done to help you sit and stand straighter, which lessens the pressure on the blood vessels and on the nerves. If you are overweight, losing some weight can be helpful. 
If the condition settles, remember that a return to the precipitating factors can cause a recurrence. Avoid carrying heavy bags over the shoulder (TOS is often called “backpackers shoulder”, as heavy weight pushes the collar bone down onto to the first rib, narrowing the TOS). 
A study with 50 patients has shown that strengthening and stretching reduced the pain in 80% of the patients after three months and in 94% of the patients after six months. Other studies demonstrated that physical therapy treatment appears to be effective in reducing symptoms, improving function, and facilitating return to work .
 Harris, D., G. Thoracic Outlet Syndrome (T.O.S). Joe de Beer & Associate: Orthopaedic Shoulder Surgion
 Franklin, G.M., Glass, L., Javaher, S.P., Kearney, R.N. (2010). Work-Related Neurogenic Thoracic Outlet Syndrome: Diagnosis and Treatment. Medical Treatment Guidelines: Washington State Department of Labor and Industries.
 Thoracic Outlet Syndrome. Physical Therapy in Onley and Cape Charles Virginia for Shoulder.