I am assuming what you have is a 'tuberous' begonia and it will require regular watering throughout its growing season.

Be careful when watering as the tuber is a saucer shape and you don't want the water to sit in the depression.
Just water the sides of the pot or better still sit it in a bowl of water for up to half an hour (subject to how dry it is)

You do not have to cut it back as such it will die back naturally.

This link will clarify what I have written here;

http://www.thegardenersalmanac.co.uk/Data/Begonia/Begonia.htm

What type of begonia is it ? there are quite a few, metallica, rex, semperflorens, etc. Derekm.