How do I care for a boston fern? It is loosing leaves and turning brown. What precautions do I take for the winter?

You are always going to have some dry browning of the fronds indoor, mainly the tips.If you just bought yours, or brought it in from outdoors. Let it do it's thing, indoor "lower light" and "humidity" can cause the browning, but you will get new growth that can take it a little better.Just keep pulling the brown fronds off and clipping the tips for now, it will get better with the right care.
Keep the soil on the moist side, not soggy wet and never let it completely dry. Let the top inch or two dry before watering it thoroughly (empty excess out) and keep it on the root-bound side.
Bright indirect light is fine.
Keep it away from all heat sources, like lamps and forced hot air etc.
A pebble tray could help with the humidity around the plant.
fertilize in spring and summer (sparingly)