How does Austen explore the importance of wealth and class in her novel in Pride and Prejudice?
I take it that the "how" of your question requires a discussion of the techniques Austen uses to explore the importance of wealth and class in Pride and Prejudice. If this is the case, there are a number of different modes of exploration that Austen undertakes. These range from juxtaposition of contrasting situations to examining details of a particular situation to exposing certain social transactions. There are far too many specifics to cover in this limited format, but we can consider some of the most interesting.
Austen exposes the social transaction that is necessary to purchase back respectability when respectable behavior is thrown aside. I refer to the transaction between Darcy and Wickham regarding Lydia and facilitated by the Gardiners. Wealth is critical in this type of transaction as Wickham's behavior and attitude demonstrate. Class is significant because a young woman in Lydia's class [upper class as a landed gentleman's daughter (do not think of Joe Wright's 2005 corruption of the Bennet's social standing)] depends upon moral respectability (or at least a reputation thereof) to be accepted in any friendship or social gathering.
"That is very true, .... His debts to be discharged, and something still to remain! ...."
One particular that Austen examines is the family of Sir Lucas. Sir Lucas was knighted and is eligible to wait upon the monarch at court. Yet, if Mrs. Bennet is to be believed, their wealth does not equal their honor. It seems Lady Lucas and Charlotte do the cooking as they do not keep a cook (hopefully they keep a maid or two!). Charlotte has a meager dowry, as do Elizabeth and Jane, which seems compounded by meager personal attractions. In this scenario, in which Charlotte's opportunities to get to London for the social season--where and when many an eligible young lady found a match--are limited, Austen examines Charlotte's philosophy of love, her assessment of her needs due to her class status, and the role of wealth in her decision of what comprises happiness and comfort.
I am not romantic, ... I never was. I ask only a comfortable home; and considering Mr. Collins's character, connection, and situation in life, I am convinced [of] my chance of happiness with him ....
Austen makes many juxtapositions of class: some are Collins to Lady de Bourgh; Lady de Bourgh to the Darcys; Lady de Bourgh to the Bennets; Collins to the Bennets. The most famous (and infamous) juxtaposition, though, is Darcy to the Bennets. In this juxtaposition (i.e., positioning of two things close together, often for the purpose of contrast or comparison), the class status of each is demonstrated, especially through the arrogant and conceited Mrs. Bennet. Bear in mind that the Darcys and Bennets are equally upper-class: both families are landed gentry; late Mr. Darcy, Sr. and Mr. Bennet are equally landed gentlemen, though their wealth, wisdom, and spheres of influence are not equal.
This juxtaposition shows the difference education and civil breeding can make, as well as the difference accumulated wealth can make. For one thing, Mrs. Bennet, for all her failings, is continually rightly worried about the future provision of her daughters who will not inherit any wealth (beyond some hundreds of pounds each) because the Bennet property is entailed from past generations away from the female line to the male line, even if that be a distant cousin. In sum, these are some of the predominant ways that Austen explores the importance of wealth and class.