How did western civilization develop the values that came to dominate the world after the year 1000? Give details.
I'm honestly not sure it's fair to say that there are "values of Western Civilization" that start as early as the year 1000. If you compare the values of modern Western nations like the US, France, Germany, or the UK, they have a lot in common with each other, but little if anything in common with the values they had in the year 1000. Equal rights for women and racial minorities would be seen as absurd in the Medieval Era, and tolerance for anything except the most orthodox Christianity was literally punished as heresy. Instead of gay people getting legally recognized marriages as they do in First World countries today, they were burned to death for their "crime" of sexual deviance. People were even burned at the stake for "crimes" as petty and absurd as believing that Jesus was nailed to the cross with three nails instead of four.
Even democracy, widely regarded as a core Western value, was not at all the norm in European society in the year 1000. Only the Nordic states (such as Sweden, Finland, and Denmark), which at the time were known as the Vikings, had anything remotely resembling democracy during that time (and really it was more like constitutional monarchy), and the rest of Europe regarded them as lawless barbarians (they were not; in fact in many ways, especially with regard to the treatment of women, they were the most progressive culture in the world).
That's not even getting into the enormous technological and economic changes since that time, without which concepts like "sweatshop worker rights" and "Internet neutrality" can't even be formulated.
What I can tell you is the values that were prevalent in Europe during this time, and where they came from---which was mostly from Christianity, specifically a very narrowly defined orthodox Christianity that would eventually become Catholicism. On the upside this meant that values like justice and charity were very important to Europeans; on the downside it meant that values like obedience and orthodoxy were equally important. Anyone who was not Christian was despised or worse, and the Pope held almost absolute power because he was literally believed to be infallible.
It wasn't until centuries later, starting in the Renaissance with the recovery of Classical Greek and Roman texts that had been preserved by Muslim scholars in the Middle East, that Europe began taking on the modern values we now recognize. So the main catalyst for what we currently call "Western Civilization values" was actually Greek culture, as transmitted through Muslim culture, and then applied by Christian culture.
Even then this was a slow process; first innovation came to be valued over orthodoxy in the Renaissance, then rationality was valued over faith in the Enlightenment, and it wasn't until the 18th century and the dawn of the Industrial Revolution that Western cultures began believing in such things as democracy and universal suffrage. We recognize the values of 18th century thinkers like Adam Smith or Thomas Jefferson as broadly consonant with our own (other than being mind-bogglingly racist and sexist); but we don't feel the same about Medieval thinkers like Avicenna and Averroes.
As for why Western values came to dominate the world, there were really two reasons, one good, one bad.
The good reason is that they were better, for the most part; democracy really is better than monarchy, rationality really is better than faith, liberty really is better than obedience. Values that work better at improving human life are values that people often like to adopt.
The bad reason is that they were forced upon everyone; by their technological, economic, and military superiority, European nations were able to conquer and colonize almost every other country in the world. They then pressed those they conquered to adopt their values, with levels of force varying from missionaries spreading Christianity to those who will listen to people being literally kidnapped and forced to attend schools where they will be taught European languages and history.