Aristotle began his metaphysical pursuit before anyone developed the word metaphysics. Instead, he used the Greek word that roughly translates into first. He defined his study as the first philosophy or the first study of philosophy. Aristotle used first to stipulate that he was studying the way philosophy should be applied or essentially developing the rules for philosophy before he tried to apply them. He established a principle for philosophy that stated that a value is best if it is being done for its own sake. For instance, if you went to work with the intention of supporting your family, but took the trash out on your way, knowing that no one would notice and just because it is right to help, you performed a higher moral act by taking out the trash because it was done for its own sake and not for appreciation or expectation.
Immanuel Kant developed his theory of the Categorical Imperative as a metaphysical study of deontological thought: the idea that the means can justify the ends and that moral justification is in the duty of the action and not the outcome. He established that a moral virtue is absolute if it should be taken by everyone universally, it treats individuals as ends and not means and if in acting out the virtue, you believe that you are establishing a universal law. Under the Categorical Imperative, you would be justified in going to work to support your family because you believe that the idea of working to support your family should be universal and the right and responsibility of every family.
John Stuart Mill established a moral justification for Utilitarianism by examining the ideas of teleological thought from a metaphysical point of view. He developed a principle of universal good that established the idea that an action is good if it produces a result that creates the most good for the greatest number of people. Mill's view of Utilitarianism reinvigorated the older philosophy with a rational justification and provided a tool for evaluation of other Utilitarian philosophies. Under Mill's Utilitarianism, you would be justified in going to work to support your family as long as your work did less harm than benefit and your family did more good than bad for the world.
Philosophers engage in the metaphysical process by evaluating moral ideologies. They can begin by evaluating existing moral establishments and then asking why those ideals are in place, such as your perception of your new job when you arrive and try to figure out why they are doing things the way they are doing them. Alternately, they can begin by asking the question "why," "how" or "what" about anything and then proceed to work toward an answer, such as when you start a business and ask yourself how you want to do business and then work to make the rules.