How can I keep yarn from dry-rotting?

I've never encountered "dry rot" in yarn that was less than 40 years old. It's more likely that you will run into problems with moths or beetles, or sunlight damage. If you live in a climate with drastic changes in temperature and humidity, your yarn should be stored in a layer of cellulose (paper sacks) to allow it to breath without felting, and then in sealed plastic to keep the bugs out. Otherwise, I recommend storing it it clear plastic bins with good fitting lids, or in sealed vacuum bags (i.e. space bags or something like that), and not exposed to direct sunlight.