Not more than one page. Concentrate. Write the important.
Address the responsible HR officer personally (not “Dear Sir or Madam”, but “Dear Mrs. Ernoult”. Just for example.)
Write one or two concise subject line(s). Not more. (You find further hints and examples in the documents linked below.
Write a concise intro too. HR officers don’t have time. Start with something that excites him/her. But do not try to be too “witty”. Avoid standardized phrases, but stay businesslike. Try to be authentic, but serious.
Highline your specific qualifications in clear respect to the offered position. What makes you appear particularly suitable for the post? Again: No standardized phrases.
Refer clearly to the call. No serial-letter-like, but custom-fit.
Mention a specific time slots. (If not given: When is the best suitable timeframe for the intern?)
Don’t forget the recipient’s address. Don’t forget the sender’s address including phone numbers. You want them to call you back, don’t you?