If you're nervous about making any sudden movements, just keep your feet planted in one place, make sure your knees are loose, and gently sway using your hips and knees.
If you're feeling a little more confident, you can subtly lift your feet off the floor. Use these small lifts to turn in a slow circle. Your date will get the hint and move with you.
Remember to keep your elbows loose, too. Dancing when your joints are locked is pretty difficult. Loose joints will make it easier for you to breathe and sway comfortably.