Kirk developed six "canons" of conservatism, which Russello (2004) described as follows:
A belief in a transcendent order, which Kirk described variously as based in tradition, divine revelation, or natural law;
An affection for the "variety and mystery" of human existence;
A conviction that society requires orders and classes that emphasize "natural" distinctions;
A belief that property and freedom are closely linked;
A faith in custom, convention, and prescription, and
A recognition that innovation must be tied to existing traditions and customs, which entails a respect for the political value of prudence.
Kirk said that Christianity and Western Civilization are "unimaginable apart from one another."  and that "all culture arises out of religion. When religious faith decays, culture must decline, though often seeming to flourish for a space after the religion which has nourished it has sunk into disbelief." 
Kirk and Libertarianism
Kirk grounded his Burkean conservatism in tradition, political philosophy, belles lettres, and the strong religious faith of his later years; rather than libertarianism and free market economic reasoning. The Conservative Mind hardly mentions economics at all.
In a polemic essay, Kirk (quoting T. S. Eliot) called libertarians "chirping sectaries," adding that they and conservatives have nothing in common. He called the libertarian movement "an ideological clique forever splitting into sects still smaller and odder, but rarely conjugating." He said a line of division exists between believers in "some sort of transcendent moral order" and "utilitarians admitting no transcendent sanctions for conduct." He included libertarians in the latter category. Kirk, therefore, questioned the "fusionism" between libertarians and traditional conservatives that marked much of post World War II conservatism in the United States.
Kirk's view of "classical liberals" is positive though; he agrees with them on "ordered liberty" as they make "common cause with regular conservatives against the menace of democratic despotism and economic collectivism."
Tibor R. Machan defended libertarianism in response to Kirk's original Heritage Lecture. Machan argued that the right of individual sovereignty is perhaps most worthy of conserving from the American political heritage, and that when conservatives themselves talk about preserving some tradition, they cannot at the same time claim a disrespectful distrust of the individual human mind, of rationalism itself.
Jacob G. Hornberger of the Future of Freedom Foundation also responded to Kirk.
more at: Russell Kirk - Wikipedia, the free encyclopedia
(good reading for everybody except McBear)