A visa allows a foreign citizen to travel to a U.S. port-of-entry and request permission from the U.S. immigration officer to enter the United States. It does not guarantee entry into the U.S.
Most non-U.S. citizens who wish to study in the U.S. will seek an F-1 (non-immigrant) student visa, but there are other visa types that are sometimes authorized for those who study in the U.S.
Once you pay your enrollment deposit to Hartwick College, you will receive an I-20 AB form that will be completed by Kaitlin Huemer, firstname.lastname@example.org, the Designated School Official and International Student Advisor. Once you receive the appropriate paperwork, you will need to sign the I-20, pay the Visa Fee called I-901 and then schedule a visa appointment with your closest U.S. Embassy or U.S. Consulate.