Firstly, you might want to check who the letter should be addressed to. You are right that the principal is the head of your college, but as you know, there are different departments that handle different day to day tasks. There will be an office in your college that is responsible for internships, etc.
Admissions, or the registrar’s office, is normally the department that keeps track of your academic career and registers you for classes, so it would be a good idea to check with them. In many cases they have a form that you and they can fill in together, so it may be worth visiting the office initially and checking if this is the case.
If you do need to write a letter, put your name, address, and contact information on the left-hand side. Leave a double line space and then put the date, another double line space and then the school name, address, and contact information.
Try to find out who the letter needs to be addressed to, leave another double space and then put 'Dear (name of contact)'.
Next is the body of the letter. It should be written in a business style such as ’I have attended college (name) from (dates) and am on (name of course). I would like to request permission for an internship of (length of time) with (company name if known).
I feel that I will gain valuable experience and knowledge from this venture and will commence my studies directly after the end of the internship.’
End the letter with 'Your sincerely' and leave a space for your signature (around five lines) then type your name in full underneath.
Good luck with the internship and your future career!