The warping you're seeing is probably already there, so it's more about preventing it from getting worse than stopping it. The first thing is to keep humidity controlled in your home, and you'll definitely notice the difference: use a dehumidifier or ventilate your rooms well, especially in the mornings. As for the furniture itself, protect it with a good varnish or wood oil every year or year and a half, and make sure it's not directly in the sun or near heat sources like radiators. For the legs, which suffer the most from contact with damp floors, put some feet or levelers under them to isolate them a bit from the floor.