simplified thumbnail:
Well, roughly, the Jews didn't conquer it. Britain did. Jews immigrated there, legally, and were contributing to positive progress, not only in agriculture, but in instituting democratic institutions and even universities. Arabs rioted over the number of Jews that Britain was allowing in. I don't think this is controversial, and (I think) Arabs and anti-Zionists would agree that Arabs started the violence with these riots. All of this increased as Jews poured in to escape German persecution during the 30's. Palestinian Arabs revolted against the British, but because of Jewish immigration. The British throttled the revolt brutally. In response to the revolt, the British limited Jewish immigration, just when Hitler's holocaust made it more necessary for more Jews to immigrate, and increasing the number of Jewish victims of the holocaust.
When the U.N. committee came in to investigate and make recommendations, the Jews cooperated; the Arabs boycotted. The U.N. recommended two states be created; one Arab and one Jewish. (If this sounds familiar, this is the same solution being discussed today. That's right, had the Arabs accepted the U.N. recommendation, the last 60 years of war could have been avoided, and the Palestinians would have a state today.) Unfortunately, the Arabs declared that if there was any Jewish state, however small, they would fight against it, and they did, attacking immediately. Palestinian Arabs fled to neighboring states by the tens of thousands, where they are still refugees today. Basically--short version--Israel won and established its borders. Jews poured in from all over the world.
Here is a map of the proposed U.N. partition that the Arabs rejected:
Then there was the Suez crisis, leading to the Sinai war an interesting side-light in the 50's. It would be fair to say that Israel attacked Egypt, in response to Egypt nationalizing the Suez canal. Israel and its allies won, but gave the canal and most of the territory back in response to U.S. and Soviet pressure.
Arab countries have attacked Israel twice since then. Both times Israel fought back and won, increasing Israeli territory, which really just makes things worse and more complicated.
After that it just gets messier and more complicated every decade.
The relationship between Jordan and the Palestinians is also complicated and important.
Also the Israeli settlement movement, in my view, makes peace almost impossible, because the direction of peace would be for Israel to give back the land it conquered, but how can you give back land when you have these passionate citizens living on it?
At least, that's how I understand it, and now everyone can tell me how I'm wrong.