I found an opening for a Software Engineering Intern position on an external job search site. The ad directed me to MITRE's career website, where I submitted my resume (without a cover letter) on or around May 17, 2010. I received an email a week later from a hiring manager, requesting to speak to me via phone to discuss the position opening.
The phone screen was conducted on May 25th, and was very basic; it consisted of questions about my skills, interests, my background in software development, and why I wanted to work for MITRE. It went well, and a formal in-person interview was scheduled the very next week. I was scheduled to speak with 3 people from 2 different divisions, and it was broken up over a 2 day period, and took place at both the Langley AFB site, and the Chesapeake site.
Day 1 (June 1st) lasted about 2.5 hours. I spoke for over an hour with the gentleman that conducted my phone interview. Most of the questions he asked were about the projects I'd worked on in school and in previous internships, and to get deeper insight into my skills and interests. The 2nd portion of Day 1's interview was with an HR person via video conference, who asked me a number of basic behavioral interview questions (like, "Why should we hire you?" and "Describe your weakest attribute"). Benefits and basic company culture were also discussed.
Day 2 (June 2nd) lasted about 1.5 hours. I was slightly late (don't forget your picture ID when entering the building like I did -_-). The questions asked were, similar to Day 1, mostly tailored towards the skills and experience I had on my resume. I also got plenty of in-depth behavioral interview questions. Everyone was very friendly, and after the interview, I received a tour of the building, and was introduced to a few people. That's a good sign, right? :)
Because my GPA was below the 3.5 outlined in the announcement (it's a 2.9), 2 weeks after the in-person interviews, I was asked to interview again, via phone, with the head of the department. This interview was more of a chance for me to explain my low GPA and to highlight the strong points of my resume and skills.
All went well, and I was called the very next day and informed that they decided to move forward, and present me with an offer.
The entire process, from the submission of my resume online, to receiving an offer, took about 4.5 weeks. If your GPA meets or exceeds what's outlined in the job description, you'll receive a decision sooner.