How is a labrum tear repaired?

Suture anchors. Your surgeon places small (usually about 3 mm) plastic or metal screws into the adjacent bone. These anchors have sutures threaded into them, which are then passed through the labrum, and tied to secure the labrum to the bone. This is done in similar ways for both the labrum in the shoulder and the labrum in the hip.
See Video. the link will give you more information and a video for reference.