Midwife's Apprentice by Karen Cushman

This is a quick read and even won the Newbery award.  The little no-one no-named orphan girl gets taken in by a midwife to do menial tasks in exchange for food and shelter. Over time the girl (who has named herself Alyce) learns skills and tries her hand at doing what the midwife does.  It's a good book about belonging and finding purpose in life despite the difficulties that seem to be in our way.