Make sure you are eligible for a multiple-entry visa. Citizens of certain countries are not eligible for multiple-entry F1 visas. If you are not certain whether your country's citizens are eligible, check the U.S. State Department's website for the "visa reciprocity schedule."
Make an appointment for a visa interview at a visa-issuing U.S. embassy or consulate. This doesn't necessarily have to be in your home country, but consular officers there are in the best position to determine your eligibility for a multiple-entry visa, because they are most familiar with conditions in your country. Check the embassy or consulate's website for information on how to make an appointment. In some cases, you may not need to appear in person but can simply drop your application off at the visa section or even send it in through the mail.
Pay the visa-application fee and provide the receipt for it and your supporting documentation to the visa section. At a minimum, this will be a valid Form I-20 signed by your university or college, nonimmigrant visa application form (Form DS-160), a passport valid for at least six months beyond your proposed stay in the U.S. and one 2-by-2-inch photograph. If you have been out of the U.S. for more than five months, you may need to pay a new Student and Exchange Visitor fee (SEVIS I-901). You can check the Immigration and Customs Enforcement website to confirm if you have to pay this fee or not.
Explain to the consular officer, either in your interview or in a letter accompanying your dropped-off or mailed-in application, why you are requesting a multiple-entry visa. As usual with any nonimmigrant visa application, you will also have to demonstrate that you can afford to pay for your studies in the U.S. and that you intend to return abroad when they come to an end.