The forward, back, and side step is simple. However, while moving around the ring, many boxers cross their legs, take long steps, or bring their feet too close together.
These bad habits must be broken in order to maintain good balance. It wouldn't take much to get knocked down while performing these bad habits. A weak punch will send you down if you're off balanced. You may not be hurt, but it counts as a knock down!
To move forward, take a small step with your LEAD leg, then bring the REAR leg up to get back into your normal boxing stance. The key is to keep your feet as close to the ground as possible. Try to avoid lifting your feet high, even if it means dragging/pulling your feet along the round. One reason is to maintain balance, the other is if you threw a punch while your feet were off the ground (or off-balanced), you would not have any power behind the pounch. To go backwards, step with your REAR leg FIRST, then bring your LEAD leg back.
To move to the side, step in the direction you want to go with the leg NEAREST that direction. Then bring the other leg over. For example, if you are in an orthodox stance and want to go left, step to the left with your LEFT leg FIRST. Then bring your RIGHT leg over to get back into your normal boxing stance. Again, do not step high as that would leave you vulnerable to getting easily knocked down.