This is an excellent Wikipedia article on the subject, from which I learned much to write this post.
The main distinctions are, as I see it, that the classical liberal believes that rights are inherent in man and negative in nature; that is, that one has the right not to be coerced through violence. (The right not to be coerced through violence is a tricky one, and I shall probably take it up in another post.) By contrast, the modern liberal believes that rights are delivered to man by government and are positive in nature; in other words, that a government can guarantee many different rights, including the right to health care, the right to food, the right to housing, the right to free speech, etc.
Much like the Utilitarianism and Social Contract Theory we're studying in my Ethics class, I find modern liberalism to be too compatible with social engineering for my taste. In my view, classical liberalism respects the dignity of each individual human being--after all, we are made in imagine Dei--and thus is far the more liberal view.
I'm not really a conservative--I'm a classical liberal. But it's probably too late to reclaim that word, tarnished by long association with an illiberal American left wing.