Well, here's basically how the process went:
We stood in line and were first interviewed by El Al security agents. They asked us the purpose of our trip, where we had traveled recently, our knowledge of Israel and the Jewish religion, etc. They were profiling us to determine which passengers had a higher security risk and needed additional checks to board. Then they stickered us and sent us through the first X-ray area. Our bags were X-rayed here and many people had thier's hand-searched as well. Then we went to the check-in counter to get our boarding passes. All the people who work in the security area are Israeli Army (as everyone in the country must serve for 2-3 years once they turn 18).
Then we went through normal airport security to get to the gate. This was another X-ray. Then at the gate, they had additional El AL security checking passports, stickers and tickets as we headed onto the plane. Additioanlly, all flight attendants are Israeli and therefore Army-trained.
When we landed at Ben-Gurion, the plane parked in the middle of the tarmac and we had to walk to a shuttle which took us to the terminal - as planes in Israel do not get too close to the terminal buildings.