Knowing the company to whom you are applying and, ideally something about the person you are writing to, can make all the difference. Do your intelligence gathering carefully.
The general process of making an application is to search for potential companies, write a generic CV/Resume, tailor your CV/Resume to each specific application using information you gain from your intelligence gathering, write a specific covering letter for each application finding out who you should be writing to, the follow it up after you have sent it.
The covering letter gets the CV/Resume read. The CV/Resume gets the interview. The interview gets the job. You can fall out of a successful process at any stage!
There are a great many online resources on CV/Resume writing and formatting.
You will need referees who will give you a good reference. If you have completed work experience before or if you have or have had part time employment your previous employers may be prepared to give you a reference. Your academic supervisor or one or two of the members of staff at your academic institution may also give you a reference if you ask. Otherwise friends, work acquaintances or your network again. Really good references are from people in the discipline area that you are applying for an internship in so if you have the choice choose wisely.
Check if there is any interview training or opportunities for dummy interviews on offer within your institution. The Careers Office is a good place to start.
Anticipate questions and plan your answers - check out a few of the more common interview questions and some hints.
Re-read your covering letter and CV/Resume - if you were reading this what questions would you have for the author - sometimes there are some obvious questions.
You will probably be given the opportunity to ask questions yourself - think about what you would like to know about the company or job, plan a few questions but don't turn it into an interrogation.
Internship Interview Questions
The Internet is a great place to look for some of the more common questions asked at interviews. Take a look at these as a starter:
Lots on interviewing, eg: http://internships.about.com/od/interviewing/Interviewing.htm
Here are a few questions you might be asked if you are specifically targeting an internship abroad:
Why do you want to work abroad (or in X country)?
What will you gain from the experience of working abroad?
Explain a time when you were abroad and has to deal with stress. How did you deal with it?
How do you cope with being abroad for a long period?
What was the most memorable difference in culture you experienced and how did you deal with it?