The U.S.A. issues different types of visas to temporary visitors, including students. As a full-time student, you would receive an F-1 or M-1 visa. Most students fall under the F1 category. The temporary visas are also known as non-immigrant visas.
The spouse and children would receive F-2 or M-2 visas.

The "F" visa is for academic studies, and the "M" visa is for nonacademic or vocational studies.

Procedure

1) Get your passport made. Follow this link for detailed information regarding how to obtain your passport.

2) Once an academic institute has accepted you for admission to full-time study, they will send you a document known as the I-20 form, which is extremely necessary for the application for a student visa. This form I-20 contains information about how much financial responsibility you will need, what is going to be the duration of your studies, etc.

3) You may need to show the proof of financial support if you or your parents are going to fund your studies in USA. A bank letter may be necessary. You might want to find out from your embassy about the types of documents they may accept regarding the proof of financial support.

Get an "Affidavit of Support" form from the U.S. Embassy or Consulate if the studies are going to be sponsored by your relatives or others who are currently in USA. Complete this form with information about your sources of financing (letter of sposorship), and submit it along with your other documents. The embassy may require a letter from the bank that holds the funds.

4) Obtain all the necessary documents mentioned on this page. Now, you are ready to go to the U.S. Consulate for a visa interview. If your visa is rejected twice, you may need to apply by mail.

Documents required for obtaining the visa

A nonrefundable application fee (You should find out the exact amount before going to the consulate and carry exact change if possible).
An application Form OF-156, completed and signed. Blank forms are available without charge at all U.S. consular offices.
A passport valid for travel to the United States
One photograph 1 and 1/2 inches square (37x37mm) for each applicant, showing full face, without head covering, against a light background; and
For the "F" applicant, a Form I-20A-B. For the "M" applicant, a Form I-20M-N.
[These forms are sent by the institutions where you have applied and upon acceptance they send you these forms.]
Sponsorship letters
Student visa applicants must establish to the satisfaction of the consular officer that they have binding ties to a residence in a foreign country which they have no intention of abandoning, and that they will depart the United States when they have completed their studies.

Maintaing Visa Status After Arrival

If a student on a F-1 visa is not able to complete their studies by the expiration date on the I-20 form, they must apply to the school's Foreign Student Advisor for an extension 30 days before expiration. Extensions are normally granted for academic and medical reasons so long as there have been no violations of visa status.

It is possible to transfer schools after arrival on an F-1 visa. You will need to notify your current school of the transfer and obtain an I-20 form from the new school. You will complete the student certification section of the I-20 and must deliver it to the foreign student advisor at the new school within 15 days of beginning attendance at the new school.

If you are changing majors at your current school, you do not need to notify the INS. If you are changing degree programs (e.g., from a bachelors degree to a masters degree program), however, you will need to get a new I-20 and submit it to the foreign student advisor within 15 days of beginning the new program.