Exchange students require four main government-issued documents during their study abroad: their passport, visa, I-94, and DS-2019. Please also visit the US government's website for more details on documents and visa regulations.
Your passport must be valid at all times during your stay and at least 3 months past the end-date of your program. Make sure to keep your passport in a secure location throughout your stay. In the event that your passport is lost or stolen, report it to the police immediately, as your government may require a police report before issuing a new passport. You will need to contact your home country's consulate in order to replace your passport within the United States. The State Department's website has a list of all Foreign Consulates.
The J-1 visa stamp in your passport permits you to request entry or re-entry in to the United States. It does not determind home long you may stay in the United States; that is what the DS2019 and I-94 are for. If your visa expires while your are inside the United States, it is not necessary to apply for a new visa unless you intend to exit and re-enter the US. You can only obtain a visa abroad at a US Embassy or Consulate. For more information on visas, plese visit the US government's website.
The DS-2019 is a document issued by your sponsor in the United States (i.e., SF State) which you will need in order to apply for your J-1 visa at a US Embassy or Consulate. A USCBP (Customs & Border Patrol) officer will stamp your DS-2019 at your first port of entry in to the United States. The DS-2019 must be valid at all times; do not let your DS-2019 expire, or you will be out of status. You should keep all DS-2019 documents forever; never discard old DS-2019s. Missing an old DS-2019 may affect your re-entry in to the United States in the future.
The I-94 is a small white card that a USCBP officer will attach to your passport at the same time you receive your DS-2019 stamp at your first port of entry. This card plus your DS-2019 permit you to stay temporarily in the United States while pursuing a full course of study. The USCBP officer will also indicate the Duration of Stay (the length of time that you are allowed to remain in the US) on your documents at this time. Do not lose this document: it costs over $300 to replace! You will receive a new I-94 each time you leave the US for more than 30 days. A USCBP will collect your I-94 from you when you exit the United States.