Make sure that your passport is stamped by the immigration official when you arrive in Jordan, whether you arrive directly or via another country in the Middle East.
Upon arrival, students who did not apply for tourist visas before leaving their country will have to purchase an (automatic) tourist visa, which requires queuing in the line for non-Jordanians and paying JD40 (about $60 USD). Since you will have to pay in JD, make sure to go to the currency exchange counter or ATM first. After you purchase the visa, you will get your passport stamped before collecting your luggage. This visa needs to be extended within the first month of your stay. Program staff will help you with the visa renewal. There is a overstay fine of 1.50 JOD per day. Getting a multi-entry visa makes sense (financially) if you intend to leave Jordan more than twice during the semester.
A departure tax of 8 JDs ($13) is paid at any border crossing except the airports.