How does Charles Dickens represent the Cratchit family as being poor?

Your question refers to the family of Ebeneezer Scrooge's employee, Bob Cratchit. While Scrooge is known for his extreme thriftiness, dark temper, and lack of charity during the "present" setting of the story, Cratchit's goodwill in spite of financial poverty is presented in sharp contrast to that characterization. We learn of the poorness of Cratchit and his family through both Scrooge's comments about them and the omniscient narrator's description of their appearance and home life.

Our first notice of Cratchit is in chapter one. In this scene he is busy in the background with his clerical work when Scrooge's nephew visits their office to invite Scrooge to dinner. Grumbling to himself after Nephew Fred leaves, Scrooge compares Fred and Cratchit to one another as people who ought to be too poor to be so happy at Christmas time.

In chapter three when the Ghost of Christmas Present takes Scrooge to observe the Cratchit family, the narrator implies that Scrooge is incredulous that the Ghost would bother to bless this family even though Bob only earns "fifteen bob a-week"; for present-day Scrooge, a person's worth is defined by economic status. The Cratchits are here described as bravely making the best of what little they have. Mrs. Cratchit, for example, is "dressed out but poorly in a twice-turned gown, but brave in ribbons, which are cheap and make a goodly show for sixpence". Their daughter Belinda is also "brave in ribbons", and their son Peter wears a too-large shirt with collars that he has borrowed from his father for this special occasion of Christmas dinner. Cratchit arrives home in this scene in his "threadbare" clothes that someone has attempted to darn and brush to make him look seasonable. The narrator also comments about the fact that Cratchit's sleeve cuffs are not capable of being made more shabby. The older Cratchit children talk of apprenticeships that will help add to the family's income, Martha already an apprentice at a milliner's shop and Peter on the verge of finding work soon. We are told that they are "not a handsome family", "not well dressed", "their shoes were far from being water-proof" and they have scanty clothing. When their dinner goose is served, the whole family is merry about it because such a dish is a rarity in their household.

Dickens balances these bits of imagery with reassurance that in spite of their poverty, the Cratchit family members are unfailingly grateful for one another's company and devotion. Their poorness is after all only financial, because they are wealthy in human kindness. The juxtaposition of the family's poverty and bravery in the face of all its hardships are a shocking thing for Scrooge to see, and this is part of the catalyst for Scrooge's decision to reform himself.