I applied online through delta.greatjobs.com, which was fairly straightforward. There is a psychological assessment towards the end. It's nothing difficult, they just want you to do it to show that you're not crazy or anything. I then had to do the video interview, which they send you a link to on your email. Nothing difficult, just simple, behavioral and situation questions. I got a call about a week later for a face to face, ended up putting it off a few times because I was also applying to be a ticketing/gate agent and wanted to get that. In hindsight, THANK GOD I DIDN'T DO THAT, ramp is so much more simple.
The face to face was fairly straightforward. At first, the supervisor came in and did some icebreakers like who we were and why we wanted to work for Delta (one girl straight up said "I'm here for the flight benefits" LOL, props to her for her guts) and then we were interviewed one by one. There was one interviewer, and his questions were fairly straightforward. It was 6 behavioral/situational questions, which needed to be answered via the "STAR" method (Situation, Task, Action, Result). Quite simple, really.
The interviewer told all the successful candidates on the spot right after the 6th question that they had gotten the job. I was thrilled, and my enthusiasm was only slightly dampened by the fact that we proceeded to spend the next 4 hours filling out paper work regarding the last 10 years of our lives. After that, we got appointments for physical exams and drug tests, and then we had 4 weeks of training and were on the job right after that!
Note: I applied first as a seasonal ramp agent, which is the process I described above, though to my knowledge, the process is the same. Around October, permanent ready reserve slots opened up at JFK and LGA, to which I applied and was accepted at LGA. The hire process for that was putting in an in-house application (you get access to the in-house only jobs on something called "e-bid" once you start working for the company in any position, seasonal is a great way to do that!), and got a call in a month saying that I had gotten the position. No interviews at all this time. Just filled out paperwork, went through like 2 weeks of training, and proceeded to start working the day after training ended.