How did Judaism regain its holy land?

Answer 1

Blood, sweat, tears, conviction, and legal precedent.

The State of Israel came together as the result of Jewish Immigration to the British Mandate of Palestine, Zionist leadership, Jewish militias and political and financial support from the West (primarily Jewish philanthropists). The first group are called the Halutzim or the Pioneers and they took it upon themselves to modernize Israel by cultivating the land and using European technology to improve its output and productivity. The Zionist leadership included some like Theodor Herzl, who envisioned the state, to Eliezer ben Yehuda, who developed Modern Hebrew as a functional language, to David Ben Gurion who declared Israel's independence and sovereignty, among many others. There were numerous Jewish militias defending the Halutzim and attacking the British (and eventually the Arabs when conflict started) such as the Palmach, the Haganah, and the Irgun. Finally, without the monetary contributions from families like the Rothschilds, there would have been no way for the nascent pre-governmental and governmental organizations to acquire enough capital to maintain an internal infrastructure.