It seems like a Catch-22. An internship is an excellent way to build your resume, but to get the internship you want, you have to have a strong resume.

When applying for a position in another culture, it can be even more difficult. The first step is making sure that your resume presents your strengths, skills, and experiences in a way that is relevant to the host organization. As you are preparing your application, pay special attention to your resume and be sure it will travel as well across borders as you plan to! The following are some suggestions for polishing your resume, IE3 style:

As a first step, visit the career center on your campus. This office will have information and resources for creating your resume. Specify that you are applying for an international internship.
Include your language(s) as skills and give an honest assessment of your ability. Don't forget English! In some internships, your proficiency in English (or another language you speak fluently) may be a unique strength.
Include your international experience. Study abroad, travel, homestays, international workcamps -- they all demonstrate that you have some experience in another culture.
Include skills you have gained through extracurricular activities. Not all your learning happens in the classroom or at work!
Include highlights from your academic coursework that are applicable to the internship site. If you have had a data analysis course, public speaking, accounting, economics, or a wide variety of other courses where you gained skills that might be helpful to the host organization, highlight it under the education section of your resume.
Be aware of cultural differences! Language that is considered "good marketing" in the US may come across as unabashed arrogance somewhere else. Know your audience!
For some countries you may have to submit two resumes -- one in English and one in the host language.
Proofread, proofread, proofread -- and then ask a friend or advisor to proofread again!

See a sample international resume from an IE3 applicant.