If they're begonias which have a corm or rhizome, dig up, remove topgrowth, leave them to dry out a bit and then store, ready for potting next spring, somewhere frost free and dry. If they're fibrous rooted bedding begonias, bin them.

You could put two or three of the fibrous rooting ones in pots indoors on a windowsill. They should flower for ages.

thanks to Bamboo and Anchorman , will investigate