Getting in touch with the professors could be the easiest way to get an internship at IIT BHU. You can send an email to the professors with whom you want to carry on your work. All the contact details of the professors and department related personnel are available on the official site of IIT BHU. Now, mailing those profs. could be a difficult and tedious task because you may not get a reply right away. A solution for this is keep sending reminders at some intervals. Also, your statement of purpose ( SOP ) should be enthusiastic, keen, and well written. If you have any prior research experience at your college, then it would be of great help. If you know some professors personally, then the chances of getting the internship are high as well. IIT BHU also offers direct internships for summers, so just keep checking their official website.
Lastly your CGPA should be quite good and you should have good recommendations from the professors at your college.