How did "robber barons" exploit resources?
It is a bit harsh to accuse the robber barons of exploiting resources since that implies that only they were doing this and that no one would have exploited resources had it not been for them. This is simply not true.
The robber barons did exploit resources. Rockefeller made his money on oil. Carnegie made his money making steel using iron ore and coal and other resources. The railroad magnates cut down forests to provide railroad ties (as well as using coal to run their trains on steel tracks). They were certainly not concerned about the environment. However, no one was concerned with the environment at that time. There was simply no sense that these resources were scarce and nonrenewable or that they might harm the planet.
So, robber barons did exploit resources by extracting them and using them to make other things. However, this was not seen as any sort of an inappropriate thing to do at the time.
You might answer the question by saying, "with great success." Or you might ask the question, "Whom did the Robber Barons rob?" You can find really greats stories about disagreement between powerful men who exchanged accusations.
For example, Edward Stokes assassinated James Fisk due to a disagreement over who should have the favor of Josie Mansfield, a show girl who claimed to love Stokes, but who had lived in an apartment paid for by Fisk.
I'm not accusing them, it was just a question for school. I have to write a paper supporting and another against industrial capitalists. I myself don't really consider them to be robber barons. Thank you for your informative answer!