The gluteal muscles are comprised of two layers, superficial and deep. The superficial muscles are what we commonly think of as our buttocks and include the gluteus maximus, minimus and medius and the tensor fascia lata.
Extensor and lateral rotation: The gluteus maximus is the largest muscle of the body. The maximus attaches to the back of the ilium (pelvic bone) and runs all the way down to the lateral sacrum and coccyx and its main actions are extension and lateral rotation of the leg. It is a strong extensor and is used mainly when the thigh is moving from flexed to straight such as sitting to standing and walking up hill. During static standing the maximus is not in use and when walking, it is used very little. Interestingly, when we sit down we are actually sitting on the tissue (and bursa) underneath our ischial tuberosity bones at the base of the pelvis, not the maximus itself.
Abduction and medial rotation: The gluteus minimus and most of the medius are underneath the maximus. Both muscles have the same proximal attachment at the external surface of the ilium and almost the same distal attachment; except that the minimus attaches to the greater trochanter slightly more anteriorly then the medius. Both muscles are used during internal rotation and when abducting the thigh. The tensor fascia lata is approximately 15cm long and enclosed by two layers of fascia and attaches to the front of the iliac crest (ASIS)  and then runs all the way down the external thigh to the upper tibia. It works with the medius and minimus to abduct and medial rotate the leg, and also works with the psoas to flex the thigh. The muscle (tensor) part also assists in stabilizing the fascia (which runs down the leg) and holds placement of the femur on the tibia when standing. These three muscles also prevent the hip from sagging when walking so play an important role with all locomotion.