Hi Mohit,

Kishore Vaigyanik Protsahan Yojana (KVPY) is a national-level scholarship/fellowship program conducted to promote and encourage highly driven students to opt for research careers in basic science courses. It is initiated and funded by the Department of Science and Technology of the Government of India. Students who qualify KVPY, known as the KVPY fellows, receive monthly scholarship up to pre Ph. D. level. 

So, basically to apply for kvpy exam you have to apply online through the official website pf kvpy by online mode.

Now, as you aske that weather yoi can fill the form from school or not, so it totally depends upon your school athourities.

If they allow you, then only you can apply from you school's computer department for this exam. 

Otherwise,  you have to go to any nearby cyber cafe to register yourself for this kvpy exam form .

Also, you have to pay a registration fees of Rs.1000(for general category) and Rs.500( for sc/st/obc/ph).

For more details and informations you can check out the official sites too. 

Good luck.