The Sherman Anti-trust Act eventually helped to break up several monopolies. It was intended by its authors to outlaw trusts that acted "in restraint of trade," referring specifically to interstate commerce. The law was very popular, passed almost unanimously by both houses of Congress.
But it turned out at first to be ineffective, largely because its language was vague. In particular, it did not stipulate that monopolies were illegal, which was the intent, more or less, of the law. In fact, in the nineteenth century the law was used more often to weaken labor unions (which, it was argued, acted "in restraint of trade") than the big trusts it was intended to break up. Some of the law's provisions were ruled unconstitutional by the Supreme Court in United States v. E.C. Knight Company in 1895.
Later, though, Progressive presidents including Theodore Roosevelt and William Howard Taft used the act to pursue their "trust-busting" campaigns against several key monopolies in the first decade of the twentieth century. So the law did not lead to any fundamental restructuring of the American economy, but it did (eventually) make it possible to limit the powers of some particularly egregious monopolies.