The front thigh muscles are called the quadriceps, and the back thigh muscles the hamstrings. The buttock muscles also are called the gluteals.
For this exercise, you need two dumbbells of equal weight, 5 to 10 pounds each. Use a light weight until you become familiar with the exercise.
To do dumbbell squats, stand with your feet hip-width apart. Straighten your legs, but don't lock your knees. Hold at your sides a dumbbell in each hand, with palms facing your thighs.
Lower your torso until the thighs are as close as possible to parallel to the floor. Straighten your legs and return to the start position. As you do each squat, contract your abdominal muscles, keeping your rib cage lifted and shoulders relaxed. Also, keep the dumbbells by your sides the entire exercise. Count one-two-three on the downward motion, and one-two-three on the upward motion. One-two-three. One-two-three. Repeat 8 to 10 times.
To avoid knee injury, it is important that you do not thrust your knees forward as you squat. Keep your body weight directly over your heels, and do not allow your knees to move forward past the imaginary line going straight up from your toes.
To practice this proper squatting technique, lower yourself with a chair behind you. Do the squat as if you are trying to sit in the chair -- but don't actually sit. Just lower your torso until the thighs are as close as possible to parallel to the floor. Then return to the standing position.