How was Israel founded?

It depends. if you talk about the ancient Israelite tribe you can say that Israel was founded by Jacob son of Isaac, son of Abraham (read from the Bible).

If you are talking about the modern state of Israel, it was found in 1948 after a long process of immigration of Jews to the area. It was officially a state only after its Declaration of Independence by the first Prime Minister of Israel , David Ben-Gurion in Tel Aviv, 1948. The Jews of Mandatory Palestine were permitted to declare this independence separately from the Arabs by U.N. Resolution 181.