How was the state of Israel created and who lived there before it became the country now called Israel?

As mentioned, the FAQ goes into it. I've gone in great detail into the creation of Israel here, which is also in the FAQ.

Note: There were "Arab Jews", but they didn't live in large amounts in the area, and really only migrated post-war for the most part.

I'd like to note that the people living in Palestine were (at the partition plan point), majority-Arab. The Partition Plan intended to create a state with a population of 60% Jews, 40% Arab, alongside a state of nearly 100% Arabs. Almost all of the Arabs already there were formerly subjects (or were descended from subjects) of the Ottoman Empire, where they had enjoyed superior status over many Jews and Christians (considered dhimmis, or inferior but protected classes). These Arabs, contrary to some popular belief, did have a concept of "Palestine", but it was a vague one at best, and not nationalistic. The concept of "Palestine" as its own entity, however, really didn't arise with the borders we attribute to it today until the British Mandate, because the area of "Palestine" was divided into two administrative zones: the Northern sector, which had the sanjaks (districts) of Acre and Nablus, and the Southern sector, which had the independent governorate of Jerusalem (directly overseen by the Ministry of the Interior in Istanbul). Palestine was included in the Syrian vilayet (province) by the Ottomans.

However, that's not to say that the area didn't have a sense of being in "Palestine", however vague it was. There did seem to have been a conception around the start of the 1900s that the people there were living in an area distinct from Syria called Palestine, though they likely considered it just an administrative distinction when the Ottoman documents said "the land of Palestine" (nationalism would not begin to rise until the Zionism movement and the Arab nationalism movements began to clash over the Mandate and how it would be divided).

So who lived there? Muslims, Jews, even Christians in very small amounts! At the point at which the state of Israel was established, the population of Jews was growing extremely fast, and made up roughly 33% of the total population of the entire "Palestine" region as we know it.

If you have more questions about the composition, nature of the conflict, or progression of the identities of both sides prior to the creation of Israel (or after!) I'd be happy to answer them :).

Sources:

Harms, Gregory, and Todd M. Ferry. The Palestine-Israel Conflict: A Basic Introduction. London: Pluto, 2005. Print.

Smith, Charles D. Palestine and the Arab-Israeli Conflict. New York: St. Martin's, 1988. Print.

Morris, Benny. Righteous Victims: A History of the Zionist-Arab Conflict, 1881-2001. New York: Knopf, 2001. Print.

And the rest cited in my FAQ post :).