Saudi Arabia is not a party to the Hague Service Convention, the Hague Evidence Convention or the Inter-American Convention, so there is no treaty route for serving U.S. process there. The formal alternative is Letters Rogatory transmitted through diplomatic channels, which is slow and uncertain; in practice, many U.S. litigants serve Saudi defendants through a local agent.
In federal cases, FRCP Rule 4(f)(2) generally allows personal delivery to an individual abroad unless the foreign country's law prohibits it, and a court can also order another method under Rule 4(f)(3). Documents should be translated into Arabic. If you expect to enforce a judgment in Saudi Arabia, take advice from Saudi counsel before choosing the method, because Saudi courts apply their own rules on recognition.