How did the American economy come to be dominated by monopolistic corporations in industries such as steel and oil?

The main reason the American economy came to be dominated by monopolistic corporations in the post-Civil War era was that these businesses functioned in an essentially regulation-free environment. The federal government, and for that matter state governments, were almost totally unwilling to pass legislation that would limit or prohibit the formation of monopolies. So steel magnates like Andrew Carnegie and John D. Rockefeller, an oil tycoon, were free to build almost total control of their industries through innovative business practices like "vertical integration," the process of buying out the supply and distribution chains in a particular industry. Rockefeller built his Standard Oil empire as a trust, which placed the stock of competitors under a central board of directors. Business leaders in many other fields, including railroads, tobacco, sugar, and meat-packing used similar methods to gain almost total control of their industries, and profit enormously. The point is that they did so in an environment almost completely devoid of regulation. 

Regulation was slow in coming, and the late nineteenth century witnessed a gradual move toward limited oversight of economic activity. The Sherman Anti-Trust Act, passed in 1890, was an early attempt to limit the power of the "trusts," as all monopolies came to be known. It was seldom enforced, however, and was only really given teeth 24 years later by the Clayton Anti-trust Act, the result of two decades of Progressive demands for reform. The Interstate Commerce Act, passed in 1887, attempted to regulate the unfair business practices of the railroads, which were of particular concern to farmers, and it achieved some success. By and large, however, the nineteenth century witnessed few successful attempts to check the power of big corporations.