You will need to make your steps quick and light without shifting much off your weight from side to side. Initially most people tend to make large distinct steps, picking up there feet, and making lots of large body movements. This is good to start with - you may need to overemphasis your movements to get to the point that they come without thinking about them. An analogy might be that one starts dancing like they stomping through deep snow, but you should eventually be more like gliding on ice. In either case, your partner should be on the opposite foot as you.
Some people teach the leader starts on the left, and the follower starts on right.
Since zydeco dance is very based on the rhythm, the first matter to handle, is to get in sync with your partner. Everyone has a slightly different style, so both leader and follower should be prepared to give some way and adapt to your partner's style. Part of the fun is to find a groove you can both enjoy. Sometimes is easier to find your partners rhythm when dancing close so I will start with that. Dancing close is done in something similar to ballroom position.