What is the best way to heal the torn tendons around my left shoulder?

Physical therapy: The exact approach depends on the degree of tear (partial vs. Total) and also on the amount of pain and presence of other symptoms. You want to avoid movements that aggravate your shoulder. Also, if the pain is severe, brief period of immobilization may be required. Range of motion exercises either at home or through physical therapy may be helpful. Pain control (pills, topical rubs etc).

Repair Lg cuff tears: If you are referring to having torn your rottor cuff tendons, a surgical repair may be warranted, especially if two or more tendons are involved, and/or retracted away from the normal attachments.