Everyone says "smooth is fast." They're not wrong. The issue with saying "smooth is fast" is that it's such a vast amount of knowledge crammed into one word: smooth. Every time I'm on the track I learn something new, and after a few years of experience this is what I've come to understand by that saying.
Think Ahead. Stay a move ahead. If you're about to apex a corner, think about where the car should end up after the turn. Anticipate what is going to happen next. This is one of those small things that greatly reduces lap times and incidents. If you're focused on hitting the apex, you've probably missed the exit. As soon as you clip the apex, you should be thinking about when to power in, and where the car needs to end up.
Be Calm. As easy as that sounds it's one of the most difficult things. When I'm agitated, my reaction time is slower, and my ability to think ahead is diminished. On the straight away, open your hands, take a deep breath, and relax. You can't be smooth if you're agitated.
Understand Physics. The biggest issue I've seen with new driviers is overworking the tires. Physics has a funny way of butting into what your inputs are trying to achieve. You can do one of three things at any given time: brake, accelerate, or turn. Do two of those three things at once and you overwork the tires to the point where they might lose traction. Brake, turn, and then accelerate. Gauge your distance, what speed you should be going, and how much traction the tires can hold and accordingly do one of those three things. When you start to accelerate, accelerate. Don't go on/off the throttle, do it once and do it right.
Be Gentle. Don't crank the wheel, don't stab the brakes, and don't mat the throttle instantly. Turn the wheel smoothly. When you start to brake, ease into it. When you throttle in, imagine you're on ice. The same idea works in reverse as well; ease off the throttle and ease off the brakes. Abrupt inputs unsettle the car, and those mistakes cause you to go into the grass. Let off the brake too quickly and the weight will transfer to the rear, which will cause understeer as you enter the corner.
Smooth is fast, and that's a true statement. At first it's difficult to know how to be smooth, and seat time is essential to learning how to be fast. It takes time, practice, and a lot of patience. Work at it, and you'll achieve what you've been working toward.