I initially applied to their "new engineering graduate opportunities" job posting via Glassdoor. It did take some time to hear back, around 3-4 weeks after my first application. I continuously updated my information on the application, as I was in my last semester of school. Don't forget to upload your unofficial transcript. I was initially looking to go into a completely different field of work after graduation (e.g. car companies) but the challenging and diverse type of works at the APL peaked my interest.
The first ever email I received from them was for an on-site interview invitation. There was no phone interview, at least with the recruiting office. Though after that first email, over the next few days a few groups from within the APL contacted me for a "phone interview", which was more of a discussion of stuff on my resume. All "technical questions" pertained to expanding upon things listed on my resume, e.g. How did you implement this? What technology did you use and how does it work? Are there any alternatives doing this? Basically understand your resume, and make sure to mainly list things you have actual competencies in. Most groups seemed unaware that the recruiting office had already reached out to me for an on-site interview, so if you are in such a situation then let the group know, so they can coordinate with the recruiting office.
About two weeks after their first email I had my on-site interview. They fly you in to Maryland, all expenses-paid (flight, hotel, car rental etc.) and reimburse you for food and transportation (if you elect to use your own car or Lyft) expanses. The hotel was probably the nicest hotel room I have ever been in. Just make sure to check out on time, if you have a 1-day interview. Also the APL campus is huge, pay attention to building numbers on the campus's map you are provided and make sure the address you enter on the GPS or Lyft includes a close building number; or you will be dropped off in a completely different entry and walk 20+ minutes.
The interview was a 1 day long interview with about 5 groups, it spanned from 8 am to 5 pm with lunch in-between. I spent a median of 2 hours per group. They send you a summary description of each group before hands. If you happen to have a phone interview with any of the groups, you can ask any questions you have about them there. The on-site interview was more of the same as the phone interview. Very easy going, more of a conversation about your background and resume and the groups. Again, most technical questions were related to things listed on your resume, or classwork you have taken etc. they also look at your unofficial transcript and may ask you questions about classes you have taken. For most groups I did 3 rotations, speaking to different group members (typically 2 people at the time). These were group leaders, sub-group leaders and sometimes prospective coworkers. For some groups, I spoke to a group of 5+ people each with their own questions. I am a recent master's graduate and I was not asked to do any presentation on my thesis, though I was asked by different groups to give an overview or summary of the work I did for my master's thesis. Most rooms seemed to have a board, which made explaining things so much easier.
As for the final offer, there was no negotiation, because it was exceptional especially considering that Laurel is a HCOL area. I received my final offer about 2 weeks after my initial interview.
Recommendation? Apply as early as possible, especially if you are within your last semester of college. From your initial application to your first day (which may require at least interim security clearance) it may take a couple of months.