Step ups are a very basic movement yet they are highly effective at improving stability and strength in the legs, and it will also sculpt you a great butt. This exercise primarily targets the glutes and quadriceps, and it will also work the hamstrings, adductors, hip flexors and calves. The core and shoulders are also assisting to hold the barbell on your back. It also has high carryover to many activities of daily living and sport.
The step up works your muscles similar to the squats, but it has some differences. The step up is usually easier to learn, and it is easier to keep a good form while doing it, since you do not need to bend your back for balance like in the squats. It also puts less stress on your lower back, because your back is straight and the step up allows you to use less weight.
Another difference is that the step up targets more of the hip extensors while the squats put more pressure on the knee extensors, although both exercise work both, the focus is different. Therefore the step up is easier on the knee joint when done right, so it might be more tolerable if you have weak, arthritic or injured knees.
Being a one-leg exercise, it will require more balance and will work more stabilizers. Since only one leg is working, don't expect to step up as much as you can squat. Another benefit is that it will help you to correct strength imbalances between the legs, since one leg cannot compensate for the other.
The step up can be done as a body weight movement on a steady chair, make sure you can do step ups with perfect form and pace before adding extra weight. Then you can progress by using a barbell, dumbbells, or a kettlebell in each hand. The barbell allows you to load heavier weight so the strength benefits cannot be denied, but it is usually harder to balance a barbell since the center of gravity is higher.
The step or box should be high enough to create at least a 90-degree angle at the knee joint when the trained leg is on the box. If the box is too low your legs won't work through the whole range of motion, making this less effective. A lower step focuses on the quadriceps, a higher step will incorporate much more glute and hamstring work, but will make the exercise harder to balance.
Keep your torso upright. Your shoulders should be over your hips through the whole movement. Don't bend forward at the waist.
Slightly bend the knee of the leg onto which you lower yourself. It takes some of the shock out of the descent and is a bit safer.
Do this exercise in a slow and controlled manner, and keep your balance the whole time. You don't want to fall from the step with a heavy barbell on your back. Make sure to keep your balance the whole time, and take at least 2-3 seconds to lower yourself on the way down. If you feel unbalanced, reduce the weight or even practice with body weight only.
Make sure the step is steady and strong. For your safety, choose a strong step, box, bench or chair that wouldn't collapse under the weight. Make sure it doesn't move or slide when you step on it.