Bone marrow examination involves obtaining bone marrow samples through aspiration and biopsy to examine the bone marrow and diagnose conditions like leukemia, myeloma, and anemia. The samples are usually taken from the back of the hip bone and provide semi-solid marrow for microscopic examination and liquid marrow for additional tests. The procedure involves numbing the skin and inserting needles into the bone marrow cavity. It typically takes 10-15 minutes and causes mild soreness for 1-2 days in most patients, while serious complications are very rare.