A bit of advice on remembering- based on many years (dammit!) experience, not just at dancing.
1)When you're shown the steps, watch actively. What i mean by this is imagine yourself doing the steps while your teacher/instructor explains them. Shift your weight onto the appropriate foot if you can, even move around a little to match the teacher- this may not be feasible. In any case, don't watch passively. You're not watching a soap on TV. This will get the information deeper into your memory at the start.
2)Write down the steps, as others have said. This is ESSENTIAL. I'm amazed when dancers go to private lessons and don't write down anything. Exactly how you write them down is another matter (which we could discuss for a long time).
3)Go through the steps as soon as you can, and later that day. Someone mentioned visualising them - this is a good technique too.
We travel many miles for our classes, and share a car. When we've been given new steps or a subtle change to existing steps, we practice when we get back to my car (a couple of hours after the class). It's in a hotel car-park, and one dark evening, somebody saw us practising some steps, and came up to us and asked were we giving classes! Life's full of little hazards!
As you improve, you will find new material easier to learn, since you can relate it to steps you already know.
Make sure you learn the names of the figures (groups of steps) too.