Depending on your field of expertise there are opportunities open to you 24/7 around the globe that will allow you to get an exciting internship.
Whether you are in Detroit, Singapore, Beijing, Jakarta, Mumbai or London you can always count on internships as a great way to gain valuable experience working with professionals. Interns are in high demand in all aspects of the entertainment industry because your unique skills have a value that can help and enhance the services of a company.
You may be a great editor, sound designer, communicator or have specific language skills and knowledge of the industry that can help companies allocate tasks to you. This can go from assisting them to cutting promo demos, to capturing sound, working on their productions as a member of the crew, providing office support and much more.
In order to apply for an internship you need to prepare a consistent CV with your skills and background (don't try to over emphasize what you can do as they will understand you are a student). Tell them why you are applying. Apply for internships that are not advertised as this gives you more flexibility in choice. Think big : Send your CV to paramount, Sony, or try contacting individuals like assistant directors through a guild or listing service such as The Knowledge Online (UK only)
Good luck and don't forget you are working for free, and you can make mistakes. Internships are there to help you learn from your mistakes, but to also improve your skills.