The I-94 is your only evidence that you have properly entered the United States. Therefore, it is important that you make sure all the information reported on the I-94 is correct each time you enter. If the information is not reported correctly, you could have tedious immigration problems later.
You will want to keep a hard copy of your most recent I-94 with your passport. Furthermore, it is recommended that you keep a copy of each I-94 issued to you in case the information from them is ever requested in the future (such as applying for legal permanent residence).
Where do I obtain it? https://i94.cbp.dhs.gov/I94/request.html
For an F-1 student, the expiration date on Form I-94 will be "D/S." This stands for "duration of status." It means that permission to remain in the U.S. in F-1 student status is granted for an indefinite period, as long as the student has a valid I-20 (see below) and continues as a full-time student. F-1 students who complete their studies have 60 days to depart the United States or apply for a change of status. Students who drop out of school without completing their educational program are immediately considered to be out of status, and should leave the United States or apply for a change of status at once.
The Form I-20 is issued by the Admissions Office of a school or university after a student has met all requirements for admission, including documentation of financial support. When an F-1 student enters the United States for the first time, an immigration officer at the U.S. port of entry will examine the student's Form I-20. The inspecting officer should stamp the first sheet of the form, enter the necessary data into the electronic Student and Exchange Visitor Information System (SEVIS), and return the stamped I-20 to the student. This form, pages 1-3, along with the I-94 (see above) is a student's primary proof of legal status and should be kept with the passport in a safe place.
The Form I-20 is also used for re-entering the United States after travel to another country. Please refer to Re-entry After Temporary Absence for more information about traveling outside the United States and re-entering in F-1 nonimmigrant status.
You may use your I-20 to apply for entry into the U.S. up to 30 days before the expected date of arrival indicated in section 5. You should plan to arrive in the U.S. on or before the date in section 5. If you are delayed and must enter after the date in section 5, you may request a letter authorizing a later entry from the International Student Advisor. You will be expected to complete your studies by the 2nd date indicated in Section 5. If you do not complete your studies and wish to continue as a full-time student after this date, you must request a new I-20 for extension of your F-1 stay from the International Student Advisor before the completion date passes. Extensions cannot be done after this date.