How does Scrooge's attitude towards Bob Cratchit and their relationship change at the end of A Christmas Carol?

Very simply, Bob Cratchit changes from being a thing to emerging as a human being in Scrooge's eyes. When the story opens, Scrooge knows nothing about his employee. He can't do without his clerk, but he resents having to pay him, and he doesn't even give him enough coal to stay warm. He definitely resents having to pay Bob for Christmas, Cratchit's one paid holiday of the year. To Scrooge, Cratchit is nothing more than a necessary machine, and he wants to keep the cost of maintaining this machine as low as possible.
That all changes when the Ghost of Christmas Present takes Scrooge to see the Cratchit family's Christmas. For the first time, Scrooge begins to understand that Bob is a human being embedded in a network of relationships. He realizes that Bob has a family to support. Scrooge especially feels for poor Tiny Tim and starts to make a connection between the young boy's probable death and the very low wages he pays his father. Cratchit loves his son, but simply can't afford adequate medical care for him.
At the end, Scrooge sends a giant turkey to the Cratchits, gives Cratchit a raise, and becomes involved with the Cratchit family, especially Tiny Tim, who does not die. Scrooge moves from using people and loving things to using things and loving people. 

In Stave One of A Christmas Carol, we meet Scrooge and his employee, Bob Cratchit, for the first time. From their conversation, it is clear Scrooge's attitude towards Bob is cold and uncaring and that their relationship is strained. Scrooge accuses Bob of "picking his pockets," for example, when he asks to take Christmas Day as a vacation. Also, Scrooge expects Bob to work in the cold office without a decent fire to keep his hands warm.
By the final stave of the story, however, Scrooge's attitude has changed significantly. Scrooge gives Bob a pay rise, for instance, and he donates a large turkey to the family for their Christmas Day meal. This kind attitude is coupled with a growing friendship between the two men, demonstrated most clearly by Scrooge's relationship with Tiny Tim, to whom he becomes a "second father."