For me, it all happened VERY quickly due to good timing but I've heard that it takes a LOT longer. On a Tuesday, I applied online--it's a very basic online application. On Wednesday, I received an email from HR inviting me to a group interview being held in Charlotte the next day. (If you live over 4.5 hours from the city of the interview, they will fly you out, but you must cover your accommodations.)
Thursday was the interview. It was SUPER LONG...8:30am to 3:30pm. I was the very last one to be interviewed. There was a panel of I think 8 PSA employees, some flight attendants and some strictly HR. We started with about 75 people. They gave an overview of the company, detailed job description including pay, benefits, scheduling, etc, and then did a question and answer session. They then told us that if after hearing everything you thought this job wasn't for you, you were free to leave. We lost about 5 people.
Next, everyone got a partner and they gave us a 15 minute break to interview our partner. We had to go up in front of the group and introduce ourselves and our partner, "sell" our partner (say why they would make a great flight attendant), and then draw a random question out of a bowl and answer it on the spot. This is their opportunity to judge your public speaking skills, personality, and response to pressure.
Then they deliberated for about 30 minutes while we waited and they came back and called the names of people they wanted to stay for one-on-one interviews. We lost about 40 more people. So about 30 of us got to stay for an interview. Before the interview, they had us complete a writing piece: they gave us a customer complaint and we had to respond as if we were the manager. The customer complaint was in email format, so I responded as if I were writing a response via email to the customer. I apologized, empathized, reassured, and offered an incentive. Also threw the company's mission statement in there.
The interview was truly 1:1. Each member of the panel interviewed a candidate so there were 8, 1:1 interviews going on simultaneously. They seemed to be averaging 20min but some, like mine, were shorter. We went over my work history (I'm a job-hopper so I had some explaining to do) and she asked me some STAR behavioral questions...talk about a time when I had a conflict with a coworker, talk about a time I handled an irate customer. What would my employer say are my biggest strengths/weaknesses, what would be the most/least satisfying aspects of being a FA, where do I see myself in 5 years. She then said she had 2 classes starting and asked my preference and said that she would email me the next day to let me know.
Friday I got the offer via email. Off to training I go.
My advice: SMILE! KEEP SMILING! DO NOT stop smiling! Even if you are nervous up in front of everyone, just smile. Even if the panel is stone-faced, just smile.