As in all other martial arts footwork is crucial in Iaido. Although not immediately obvious, how one moves his/her lower limb dictates the effectiveness of the sword movements (re: blog published 18th Sept 2017 titled "Ashi, Koshi, Katana"). Most schools nowadays often leave out this part of the training, yet expect the students to somehow picks it up on their own. If you have experience in Aikido or Karate, they do emphasise the footworks quite extensively. In Iai, this is not immediately obvious until that one day you realise your sword strikes seem unstable, or your body bobs up and down or sway side to side way too much.
There are a few exercises that are important. Different from Aikido or many other forms of martial arts, when in a forward stance, the foot in the back should point forward parallel to the forward foot. The heel of the rear foot should also be on the ground as much as possible. Front knee bent, and back knee straight. width of one's stance should be about shoulder width, and never not wider.
When moving forward, never stomp. Glide just above the surface of the floor while keeping the centre of gravity directly below the mid-point of the pelvis. Avoid bobbing up and down, so when viewed from the side, the shoulder and head moves smoothly in a horizontal line. When viewed from the front, your body should face forward at your opponent and not obliquely as often done in Aikido as Han-mi (半身).
These movements are basic, yet often done incorrectly. I was taught to do the same on one knee when I first began. Once I have gotten used to that, then I was taught to walk as described above. There are other movements including turning to the side and turning 180° around. Always maintaining balance and keeping the centre low and stable. When you can do this, your sword strikes will improve. Failing this, your opponent will easily knock you off balance and your life ends with his sword cutting though you.