How does someone know if they have tuberculosis?

See your doctor. Symptoms of pulmonary tuberculosis include fever, night sweats, cough, and weight loss. Your doctor can place a skin test, get a chest x-ray, and get sputum cultures if s/he suspects tuberculosis.
Cultures... If a person has been exposed to tb, a skin test will usually be positive. If the person then has symptoms of active TB like cough with sputum (can be bloody), fever, night sweats, weight loss, etc., a sputum sample is sent to the lab where the TB organism can be isolated. Once the sputum culture is positive for tb, the diagnosis is made.
Chronic cough. Most with pulmonary (lung) tuberculosis will have a chronic cough, but other things can do this as well. Intermittent fever, bloody sputum and night sweats increase the likelihood. You can get a TB skin test to help rule this out.