What methods are used to reconstruct the breast after a mastectomy?

Various techniques. Techniques for breast reconstruction have changed over the years. Most reconstruction is implant based -- either using a tissue expander to help stretch the muscle and skin before using an implant, or direct to implant reconstruction. Surgeons can also use flaps which transfer soft tissue, +/- skin, +/- muscle. These may come from the belly, the back the buttocks or the thighs.
Your & MD choice. Postmastectomy breast reconstruction options are dependent on the patients body habitus, the need for postmastectomy radiation or chemotherapy, the patient's wishes and your plastic surgeons recommendation.All this gets discussed at length in your consultation as your surgeon will have the luxury of examining you and identifying any areas of concern that may impair use of one choice over the other.
Implants vs. "Flaps" In general, there are two types of reconstruction following a mastectomy. One type involves placing an inflatable balloon under the chest muscles and slowly inflating it over weeks-to-months, followed by placement of a permanent implant. The other method involves transplanting tissue from one part of the body, such as the abdominal wall or back, to the chest wall ("flaps").