I don't think there are any hard and set rules about how to get an internship. Your school may have lists of available opportunities, or even on-campus interviewing sessions set up. From your end, you should identify companies where you'd be interested in interning, then call and ask for the human resources department (for bigger companies) or the hiring manager (for smaller ones). Tell them about yourself and what you're looking for, and they'll put you in the right hands.

You're studying media, so don't forget about online internships. I'm a food blogger and I know a number of new food bloggers who are interning with more established food blogs to learn the ropes. If you need school credit you might need to work things out with the school, but if it's just for your resume and your experience, a blogging internship might be very useful.

Hope that helps, and good luck. Let us know where you end up!

Erika gave you some great suggestions. I would add to that and suggest that you research each company in which you're interested. Review the content of their web site to determine which aspects of the business falls into your background. Find the person to whom you should address your request. Make it known that you are knowledgeable about and have much interest in the company. Indicate that although you hope to learn from them you also believe that you have much to offer as well. Discuss your strongest points and how they correlate to the business. Convey your enthusiasm.

Make sure your letter is well written and professional in its content and presentation. Let it sit a day then read it again. Be sure to proofread!

Good luck to you!