To provide a single definition of conservatism in today's world seems as hard as trying to describe the meaning of "liberal", but there are some basic factors that make a particular person or political ideology "conservative". These commonalities date all the way back to the French Revolution, which was the foundational experience of modern conservatism. The declaration of war against France's existing order by people inspired by revolutionary liberalism is rightly regarded as the beginning of modern politics.
The French Revolution's impact cannot be overestimated, and one does not need to know much detail about it to see this, so long as we generalize slightly. Before the revolution, there was no such thing as conservative ideology because there was no need for it: society and politics changed mostly organically, and with the exception of utopian religious movements like the Anabaptists no-one proposed revolution.
Then along came revolutionary liberalism, with standard-bearers like Thomas Paine, declaring that they had used the power of their minds to discover a form of government that was morally and practically the best form possible, and that it looked nothing like society as it existed right now. This of course alienated adherents from their surroundings, and led them to want to overthrow the existing order to enact liberal democracy; this was the idea that lay behind the French Revolution, and the subsequent attempt of the French to spread their doctrine throughout Europe. The argument was so convincing that the philosopher Hegel declared the Battle of Jena, when France defeated the Prussians, to be the end of history. "Liberal" here, it must be noted, means something quite different to "left-wing", a term with which it is often conflated today.
Modern conservatism grew in opposition to the claim of revolutionary liberalism to have discovered the best form of government by brainpower. It sanctified the social and political order as it actually existed in the here and now, opposing change which came from the vantage point of some imagined utopia. While conservatism was of course a justification for those who enjoyed power and advantage in society to keep it, this was clearly not all that it was - just as, I should think, no-one would dismiss liberalism as merely a naked power grab by the disadvantaged. Conservatism gained immediate traction due to the incredibly bloody experiences of the French Revolution and the subsequent wars, which made it clear that projects of radical political change would always be accompanied by violence on a massive scale.
Conservatism was supposed to be sensible and pragmatic, questioning grand schemes to improve the human condition. It is essentially pessimistic about the chances of any wholesale change in this condition, and looks askance at liberalism's idea that history is the story of the progress of humanity's moral and material condition in the face of repression. Conservatism is guided much more by a fear of anarchy and the complete breakdown of order - which, after all, we also need to be truly counted as free - than it is by the promise of "progress" that guides liberalism. Progress is reversible and a constant battle, conservatism says, and too rapid a rate of change can destroy existing gains. Conservatism hence caters to the part of us that wants safety and security rather than the promise of a better tomorrow which comes at the price of the safe today.
Of course, drastic change to traditional social and political organization became inevitable, and happened gradually over the course of the nineteenth and twentieth century until full political emancipation was achieved. Along the way, conservatives learned to accept the rate of change but argue that it should happen organically and in line with the traditions of the nation rather than being imposed by a sudden and all-encompassing revolution. Along the way conservatism morphed briefly into its more aggressive variant, fascism, and in its mainstream moved so far away from the traditions that it originally defended that it became unrecognizable on the European continent.
Conservatism's stance on "isms" is consistent. Although Nazism is often understood as an extreme variant of conservatism, this is not true. Nazism and Stalinism had in common that they were projects that aimed at a complete transformation of existing reality, and they are hence radically anti-conservative. Likewise, capitalism is strongly questioned by true conservatives because it is itself revolutionary, constantly making and remaking the world and society as technology and development advances. Right-wing political parties that embrace free market policies owe their economic policies much more to liberalism than they do to conservatism, which has placed them in a paradox from which none have managed to escape as their economic policies and the new ideas that they engender often undermine the goals of their conservative social and cultural policies.
Likewise, "neoconservatism" is not strictly speaking conservatism. The idea that Iraq could be invaded and fundamentally reformed and transformed into a liberal democracy was anti-conservative. The traditional conservative view on international relations is realism, the idea that a state must largely make do with the world as it is rather than trying to transform it. Liberalism, on the other hand, was originally militantly evangelical, traits that it shared with Communism and Nazism, before settling on its later distrust of military force and desire to focus on improvement at home rather than adventures abroad. The war in Iraq hence showed the extent to which modern politicians combine liberal and conservative traits, and explains the peculiar antipathy held towards neoconservative intellectuals by many traditional conservatives.
It was conservatism that also gave the modern age its peculiar fascination with history. If liberalism claimed to be universally applicable - a form of natural law - then conservatives claimed instead that what was actually universally applicable was the relevance of the particular circumstances by which a particular people had developed into the state they were in now. Conservatives discovered the historical dimension to reality and sanctified it, whereas liberals had little use for the past except to show how the emergence and triumph of their own ideas had been inevitable; this became Whig history.
In opposition to the unhistorical "rights of man", conservatives discovered the "Rights of Englishmen" and the "Rights of Frenchmen" whose development they could trace over the centuries. By pointing out the successes of the established order in creating stability and freedom within a structured society, conservatives hoped to defend the established order and discourage anyone from wanting to overturn it. Patriotic myth attempted to fill a psychological need for identity that liberalism also made a claim on, effectively asking people to trade the safe humility and equality of being just another man among men for the glorious duty of being (say) an Englishman who stood unique among men.
Conservatism, then, is not the same as being "right wing". The tension between conservatism and liberalism is one of the great paradoxes of modern political discourse, similar but not identical to the one between liberty and equality. It is an argument from which no politically active person can be absent, and it certainly does not permit of an easy choice between one or the other; without the mediating influence of the other force, both conservatism and liberalism would lead us quickly to disaster.
By participating in the political and social system as they exist rather than seeking to overthrow them, we all betray a degree of conservativism and an understanding that workable institutions must develop over centuries rather than being wished into existence out of whole cloth. Without staying anchored in reality and appreciating the history of the institutions that brought us to our current stage of development, mankind has shown that it is capable of a quick descent into utopian wishful thinking that inevitably ends in the slaughterhouse as it runs up against the constraints of reality. Just as conservatives ought to acknowledge the power of the human mind to improve reality and dream of a better tomorrow, liberals would benefit from a more reverential appreciation of today. Given the alternatives that we can see in the annals of history, and how quickly everything we have can be lost, we are not doing so badly after all.