How can an engineering student apply for summer or winter internships at top B schools like IIMs/ISB/XLRI, etc.?

You need to keep in mind that the internships at top B schools such as IIMs/ISB/XLRI will be strictly literary and not industrial. If you are interested in such things or your college does not have any strict criteria of doing only industrial internships, then you can definitely apply at these institutes.

Whenever you want to do an internship, start applying at least a month before the start of the internship. During the summers many professors are out of India or are on vacations or are attending some seminars, so apply as early as possible.

The process of application is as follows.

• Search for projects or departments in the institutes which suit you and your interests.
• Then look for the professors in your interested areas and find out their email IDs. This is simple and you can get all their details on their respective institute websites.
• Send in your cover letters and CVs/resumes to them through e-mails. A cover letter should explain your interest, why you want to do the internship, your expectations, any prior knowledge if you have any, and other such details. CVs inform the professors about your academics, achievements, etc.
• After sending the emails the only thing you can do is wait. You may get lots of negative responses. Some professors may even take some interviews or other tests or tasks.

You may even get a stipend which such internships.