How do I get an internship at a fashion magazine?

I'm not 100% sure if you're interested in fashion in general or working at a fashion magazine, but assuming you want to work at a fashion magazine, I would say that it's very competitive, but if you are persistent and talented, it is definitely possible.

Start with a list of magazines you admire and send your resume to their Human Resources department. They will keep your resume on file if position are open or if positions open up. However, many publications do not take hire high school interns, so be sure to check out whether college is a pre-requisite to the internship. Are you interested in writing/editing or another aspect of the magazine? To get your foot in the door, try your hand working at smaller publications, for example your high school newspaper, yearbook, literary magazine. This will give you very valuable experiences and make you more familiar with publishing.

Larger publications, like those within the Conde Nast family, are harder to get internships without previous experience or having a connection. To get your foot in the door I'd look into smaller but well known magazines like Bullett Magazine, Nylon Magazine, Paper Magazine, etc. Call their offices and speak with the front desk or administrative assistant. Let them know you're highly interested in an internship position and that you'd like to know where you can send your resume and cover letter. Magazine offices are very busy so if you don't hear back in a week call back and follow up.

You might want to check out this site: http://www.fashion.net/howto/fashioneditor/ for tip on how to pursue a career as a fashion editors. Also check out this site: http://www.fashion.net/howto/fashioneditor/http://dailyfashionjobs.com/http://www.fashion.net/howto/fashioneditor/ for jobs posting in fashion.