Slik, the modern state of Israel was formed in 1948 after a decades-long process of preparing the ground through Jewish immigration to what was then (on paper) Ottoman-controlled Palestine. Zionists had been very active in calling for a Jewish state since the late 19th century and had been given a sympathetic hearing by the British government, which was very influential in the region.
Any number of websites can give you the basics of this process. Are you interested in some particular aspect of it?