Boltonjohn,
it all depends on what sort of begonia you have, if it is a
tuber you can cut it into pieces as long as you have a shoot forming on each piece, make sure the cuts are dry before you plant them in compost and don`t cover them
completely or they will rot.
If it is a root begonia you can propagate by taking cuttings about 3inches (8cm) long let the ends dry before putting in compost or put in water and pot up when roots have formed. good luck