For me, the smoothness comes from use of my feet and - to a slightly lesser extent - my ankle, knee and hip joints. To make it easier, I'm going to use a forward step to describe what I mean
There are a number of different ways to think about the motion, but they are all striving for the same effect. I think about taking a step and rolling through the foot in a controlled manner, not simply dropping from heel toe. Experience has taught me that to do this, I need to soften my knees to a point where I'm not collapsing, but they are not locked. I sometimes think about using my knee to absorb the weight that I am transferring forward. I also need to keep my core engaged, because when I soften those muscles, there's a definite 'plopping' from foot to foot. There are about a million more things, but for me, those were the biggies.
To be able to do this, I needed to strengthen the muscles in my feet (hello, foot raises), learn how to activate my glutes so I didn't fall over while in the split-weight transition point, and practice when to transfer my body weight from foot-to-foot. I used to do it too early, which made things jerky.
Exercises that might help: foot raises, simple walking concentrating on feeling every muscle in your feet work - landing on your heel, softly lowering, then pushing off of your toe -, long steps back and forth passing your feet (keep one arm on a wall at first, if you need to) concentrating on finding your split weight position and how (and when) you move your body weight over your feet. You can also do this last one with a focus on toe release going backward and using your standing leg to absorb and push, as appropriate.
