Hi, thanks for a great an important question. The most important work on this topic in recent years is a book by Professor Liora Halperin titled Babel In Zion. However, before I talk about some of the research in that book it's important to cover the more conventional narrative of the rise of Hebrew in Israel/Palestine–basically what a bright highschooler in Israel might tell you, which has a good deal of truth to it, but also oversimplifies at some points (which I'll get to at the end).
So the modernization/resurgance of Hebrew predates zionism or even protozionism . already in the 1850's enlightened European Jew, especially in Eastern Europe, (generally called Maskils) are starting to increasingly use Hebrew, albeit mostly as a literary language. I'm not sure to what degree these intellectuals (such as Moses Hess) were consciously trying to "modernize" the language, but regardless, by simply using it they were having to find ways to express new concepts in a language which was poorly equipped for the task, hence resulting in neologisms, changes to grammar etc. In addition, Eliyezer Ben Yehuda, who is often credited with modernizing Hebrew was already living in Palestine and publishing a Hebrew newspaper before the rise of the Zionist movement. Finally it's important to remember that many Jews (unfortuantely mostly men) around the world had a good deal of knowledge of Hebrew from reading traditional Jewish texts, and would often resort to using Hebrew as a means of communication when interacting with foreign Jews–so it's not like the revival of Hebrew was the same as Esperanto, something created completely Ex Nihlo.

A lot of these intellectuals ended up in the Hovvei Tzion groups in Eastern Europe (literally meaning lovers of Zion) which predated "Zionism." The most famous of these individuals was Ahad Ha'am, who considered the revitalization of Hebrew as central to the reinvigoration of the Jewish national spirit. When members of these groups moved to Palestine (in what is now called the first Aliyah) and setup a number of agricultural settlements, they often tried to use Hebrew, but typically had to use Yiddish to communicate. Although for a number of reasons the settlers of the first Aliyah, these "lovers of Zion" were/are considered in the conventional narrative as "less ideological" or less nationally committed than later "zionists" (especially where Hebrew is concerned), they often did put a great deal of importance on Hebrew. In fact the first school to teach Hebrew in Palestine was setup in Jaffa by members of this group.
However, it is the second Aliyah which arrived between 1904-1914 (at which point political Zionism had already begun) is traditionally, and not without merit, credited with really making spoken Hebrew an issue of primary national importance. Not only did the farming collectives of the second Aliyah (later called Kibbutzim) operate in Hebrew, but the most fiercly nationalist of the youth was quite militant about enforcing Hebrew as a spoken language. promoters of Hebrew would bully people in the streets when they heard them speaking Yiddish (or latter German or other European languages) and some Yiddish institutions were even attacked or burned down.

Of course, Hebracization didn't happen overnight, cities were always locations of more diverse linguistic communities than agricultural settlements, and with later immigrations (such as the German-speaking fourth Aliyah, or the aliyah from Arab countries after the founding of Israel) there were serious "setback" and even fears that these other languages would supplant Hebrew, but the high level of national importance settlers in Palestine gave to Hebrew, along with the fact that the most important national institutions (the hishdadrut, the army, the Kibbutzim) all prioritized Hebrew and basically required Hebrew eventually resulted in Hebrews ascendency...

Now back to the most recent scholarship on this matter, which complicates this narrative a bit. Basically Babel in Zion argues that even while Hebrew was given incredible national significance by members of the second alliyah, there was spaces where other languages were considered permisable, even by otherwise fierce ideologues. Basically members of the Yishuv (the pre 1948 Jewish community in Palestine) were doing a sort of code switching (not a word Halperin uses in her work, but I don't imagine she would object to it) where areas seen as important to the future of the nation require Hebrew, but areas seen as frivolous, comedic etc. became sights of use for Arabic or Yiddish.

Finally, I will add, even in the areas which were supposedly completely "Hebracized" by 1948, it's not what one would expect today from a national language. Army reports in 1948 are full of typos, Israel's first president's wife, Vera Weizmann couldn't speak Hebrew etc.