A person born in Israel after the establishment of the State acquires Israeli nationality by birth when a parent was an Israeli national; birth in Israel alone to two foreign parents is not general jus soli under the Nationality Law.
A spouse of an Israeli naturalizes under the Nationality Law (not the Law of Return) over roughly a four-and-a-half-year graduated process.
Every Jew has the right to come to Israel as an oleh under the Law of Return; the same rights extend to a child and grandchild of a Jew and to specified spouses, subject to the statutory exceptions. Separately, the Nationality Law transmits Israeli nationality through an Israeli mother or father.
Sources: Israel Law of Return 5710-1950 (published text) · Israel Nationality Law 5712-1952 (amended text)
A non-national adult may naturalize while in Israel after three years of presence out of the five years before application, permanent-residence entitlement, settlement or intention to settle, some knowledge of Hebrew, and renunciation or loss of prior nationality upon naturalization.