There may be slight variations depending on the type of analysis you are applying to work on but overall they are looking for critical thinking skills and the ability to clearly express yourself.

After the application, about 2 weeks later I received an invitation to take an online assessment and write some essays. First was an online skills assessment which consisted of mainly logic games, like how would this unrolled six-sided figure look if rolled back up. Then a behavioral test with psychological questions. After another 2 or 3 weeks, I received an invitation for an in-person interview. They fly you out to DC for an in person interview. Before going, they ask for more essays. You are responsible for booking everything and the perdiem they give you in the form of a gift card is less than the GSA rate so go cheap in your hotel. At the interview, they group you into pairs of four or five and deliver a presentation initially on why the CIA is great. This takes about 30 minutes. After that there is a group information session about the specific position you are being interviewed for with a higher up from that division of the agency. This takes about 15 minutes. Finally, you go into a two-person panel interview where they trade-off questions. There was only about 6 or 7 questions and they all behavioral, none were technical, mainly focused on people management and "fit". After the interview they send you off home. I'm guessing if they really like you they ask you to stay or not. I received an email notification about a week later that I didn't get the job. Kind of crazy they fly you out for a touch time of about 45 minutes to an hour. I thought my answers were cogent and got to the heart of the challenges in the government, i.e. the people and the red tape. But I guess with my private sector experience, I didn't make a good fit for a paper pusher.