If cured, keep onions in a well-ventilated place away from heat and light. A hanging basket away from a window works well. Watch out for other items, like potatoes, as onions emit ethelyne and cause items to ripen or sprout. They'll typically keep for 3-4 months.

If fresh/spring, store in the fridge in the crisper drawer and they'll last for a couple weeks (though the greens may wilt sooner)