Assuming you're growing the cauliflowers yourself, this advice applies to after harvesting. Keep the roots intact and shake off the soil. Hang the cauliflowers upside down in a shed or similar place which is both cool and dry. They will stay firm for up to 3 weeks if stored like this. If you want to keep the cauliflower firm in the kitchen, keep refrigerated in the vegetable crisper and use within the week.