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

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.
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).

Related Questions

What is the best way to heal the torn tendons around my left shoulder? I feel no pain. I've had this problem since last year april. Tried physio

Therapy for strength. You need to re engage normal strength and range of motion, otherwise you are looking at a lot of disability down the road.
Surgery likely next. Having failed physical therapy, tendon tears about the shoulder (rotator cuff tendon tears) will likely benefit from a surgical repair. A thorough evaluation by your orthopaedic surgeon will help delineate whether surgery is the best option in your particular case.