If they're fibrous rooted begonias - the small bedding ones - there's not a lot you can do for them. You could try to overwinter them indoors or in a greenhouse, but I've not been very successful at that.

Assuming they're the larger begonias that grow from a tuber, you dig them up, clean off soil as best you can and allow the top growth to die off. When the stems have detached from the tubers you store the tubers in a cool dry place until spring. Some people put them in dry sand or compost, I used to put them in a single layer in an empty seed tray on a shelf and keep frost free.

I found that vine weevil grubs love these tubers in storage, so inspect them from time to time and remove and squish any grubs you may find. I used to dig them out with the end of a teaspoon.

In the spring you can start the tubers growing again by putting them on compost and not quite covering them, and water lightly until growth starts.

I don't grow these any more, as you may have noted - great plants, but different gardens need different planting! :-)

Thank you Beattie, as i say i had never grown them before then i saw them in a friends garden ,and i fell in love them,.I appreciate your help . Margaret :-))

Which sort do / did you have NM? I had both sorts in a shady garden and they did really well.