Saudi Arabia has 3 international airports at Riyadh, Jeddah and Dammam. The airport at Dhahran is now closed to civil traffic, so passengers to the Eastern Region now fly into Dammam, or into nearby Bahrain (which is much better connected) and then cross into Saudi Arabia by car.
Saudi Arabia is served by the national airline Saudi Arabian Airlines, often referred to by its Arabic name Saudia. Saudia has a reasonable safety record, but many of their planes are on the old side and the quality of service, inflight entertainment, etc. tends to be low. Virtually all Gulf airlines and most major European airlines fly into Saudi. During the Haj, numerous charter flights supplement the scheduled airlines.
Foreigners living in Saudi Arabia can often get sensational discounts on outbound flights during the Haj. Airlines from Muslim countries are flying in many loads of pilgrims, and do not not want to go back empty.
Infrequent passenger ferries run once a week or less from Egypt and Sudan to ports in western Saudi Arabia. Slow, uncomfortable and not particularly cheap, these are of interest primarily if you absolutely need to take your car across. An unofficial ban on Western travellers may still apply.
There are no railways connecting Saudi Arabia with other countries.
The principal international routes from Jordan are Amman to Dammam, Medina and Jeddah. There are also roads to Yemen (from Jeddah), Kuwait, Qatar and the United Arab Emirates. A causeway links Al Khobar with Bahrain. There are regular international buses between Saudi Arabia and Bahrain, Egypt, Jordan, Qatar, Syrian Arab Republic, Turkey and United Arab Emirates.