As for the title of the question, why it costs so much: A fundamental difference between the US and other countries (or the US several decades ago) is that the rest of the world believes that education is a communal responsibility that should be paid for in large part by tax money. As a consequence, many countries have no tuition costs to students at all -- for example, during my college years in Germany, I never spent a single Deutschmark on paying for college: it was all tax-payer funded.
In contrast, contemporary American society has come to accept that taxes are bad and that many things are an individual responsibility. States no longer pay a substantial share of universities' operating costs, and so the majority of what it costs to provide students with an education needs to necessarily come from students themselves. That adds up to thousands of dollars per year per student. (A back-of-the-envelope calculation will show that that is not much more than it is in countries like Germany, for example; the difference is only who pays for it.)
Given this, it makes sense that you may be able to find opportunities to get a college education for more or less money, but you will not find much if you're looking for "essentially free" education. It simply costs $s to educate students, and someone has to pay for it whether that's at Harvard of Podunk Community College. The only approach you can take is to be good enough to get a scholarship: It that case, your education orof course still costs money, but it's not you but some scholarship fund that will pay for it.