Pot up your plants and grow them on under glass until all risk of frost has passed. Water well after potting up, and while keeping them in a bright, warm spot, only water again when the soil becomes quite dry.
Once actively growing, they can be watered more regularly, especially those growing in sunnier positions, but make sure that the compost or soil is never overly wet or waterlogged. During the growing season they can be fed with a balanced liquid fertiliser.
Begonias grown in the ground should be lifted before the first hard frosts and left to die back before being stored in a well ventilated, dry place over the winter. Container-grown plants should be brought under cover during winter and 'potted on' into a slightly larger container each year in spring.