I consider myself to be a classical liberal (free trade, freedom of expression, freedom of religion ...)with an exceptionally large bleeding heart (there is no excuse for having hungry kids or the mentally ill out on the streets), but I am trying to understand what it means to be a libertarian.My advice: I recommend Arnold Kling's Learning Economics, which is available on the web, here. But I would like to deal directly with the student's implied question, which seems to be how the "less fortunate" would cope under a regime of liberty.
The student implies that there is a tension between liberty and what he or she might call "fairness." The idea seems to be that some kids are hungry and some mentally ill persons are homeless because . . . because what? Because persons who are not hungry or homeless have taken food and health care from the hungry and homeless? No, that can't be the answer, if you understand that the economy isn't a zero-sum game.
Perhaps the hungry are hungry and the homeless are homeless because those who are "more fortunate" aren't paying enough taxes to provide for our "less fortunate" fellow citizens? On the contrary, taxes (and regulations) stifle economic growth, which benefits everyone who is willing and able to work. That includes the parents of children who might otherwise go hungry. That includes persons who are prone to mental illness but who would have greater access to health care, given a job and/or health-care benefits.
So, a regime of liberty would actually be to the advantage of most of the "less fortunate" among us. The "least fortunate" would benefit from private charity, which is stifled by the present regime, which I call the regulatory-welfare state.
For more about the effects of the regulatory-welfare state on the general welfare, go here. For evidence that taxation suppresses private charity, go here and read to the end.