I will focus on how these characters are introduced in the novel rather than give you a detailed account of what they do in the first book. Introducing characters is something that is done particularly well by Dickens and his introductions always manage to give us a very clear idea about who they are and their general characteristics.
Thomas Gradgrind is characterised in the very first chapter by his utilitarian philosophy and the reliance on facts in his philosophy of education:
"Now, what I want is Facts. Teach these boys and girls nothing but Facts."
As the first chapter suggests, everything about his rather austere and foreboding appearance underlines and emphasises this maxim, showing Gradgrind to be a man divorced from emotions and feelings.
We are first introduced to Louisa in Chapter 3 when she goes to see the circus, "to see what it is like." Being brought up by their father's educational philosophy and ideas, Dickens tells us that:
...struggling through the dissatisfaction of her face, there was a light with nothing to rest upon, a fire with nothing to burn, a starved imagination keeping life in itself somehow, which brightened its expression.
In spite of her father's attempts to teach her nothing but "Facts," it appears some lingering remembrance of the power of imagination struggles on.
When we think of Bounderby, he is introduced in Chapter 4 in ways that make clear his arrogance, his pride and his power:
A man with a great puffed head and forehead, swelled veins in his temples, and such a strained skin to his face that it seemed to hold his eyes open and lift his eyebrows up. A man with a pervading appearance on him of being inflated like a balloon, and ready to start. A man who could never sufficiently vaunt himself a self-made man. A man who was always proclaiming, through that brassy speaking-trumpet of a voice of his, his old ignorance and his old poverty. A man who was the Bully of humility.
He literally has a "big head," and by describing him as the "Bully of humility," Dickens prepares us for Bounderby's endless fictions about his childhood used to justify his harsh treatment of his "Hands."