(Sharing this in a blog post as several people asked me for internships on LinkedIn.)
For internships you should contact the recruiter associated with your region and university. You can find this person on the Microsoft career website. Go there:
And select “Student or recent grad ->” (United States). Then on the top right corner, select “Find Recruiters & Events”.
If you do get in, there is a big interns community at Microsoft and the internship experience is amazing (I have not gotten the chance myself but I managed and mentored several interns at Microsoft).