Her article at the NCIS wiki (link below) has all the information you need.
To sum up, Ziva is a former officer of Mossad (the Israeli intelligence service) who was first at NCIS as a liason between the two agencies. This lasted for a few years; then she and her father had a falling out (long story; details in Wiki article) and Ziva left Mossad. She then applied to become an NCIS agent and her application was granted. She first became a probationary NCIS agent, contingent on her becoming a US citizen. After she took her citizenship oath, she became a full-fledged official NCIS agent.
Those are some of the highlights. The NCIS wiki article has a lot more detail and should tell you everything you want to know. Hope that helps!