There are about a million different types of squats, but for the purpose of targeting your glutes, choose between the front squat, back squat, or goblet squat and load on the weight. You'll activate your glutes, hamstrings, quads, calves, and core, building strength through your entire lower body while also developing bone strength and coordination.
Regardless of which squat version you choose, the basic form remains the same. Start with your feet roughly shoulder-distance apart, your toes angled slightly outward. Tighten your core and start the squat by pressing your hips back, as though you were going to sit down in a chair. As you press your hips back, begin bending your knees to lower your glutes toward the ground. Make sure you're keeping your weight in your heels and your knees aligned with your toes without jutting in front of your toes. Drop your hips as far as you comfortably can (there's no need to take them all the way to the ground), then press through your heels and return to standing, pressing your hips forward at the apex of the squat, squeezing your glutes.