You are probably still harvesting plenty from the veg garden with Carrots, Lettuce, Broccoli and Calabrese all still producing well. You may even be lucky enough to still be picking a few late Runner Beans.
Cut them away from the plant with a small length of stem attached and leave in the sun or in a warm dry shed or Greenhouse if the weather is wet. Make sure there is plenty of air around them.
When the skin hardens and the fruit sounds hollow when tapped they can be stored in a dry, cool but frost free place.
Winter squashes such as butternut types, keep the longest but need to be kept very dry and not too cold, an unheated room in the house or the cupboard under the stairs is perfect.