From my experience, you need to go to the ministry of Information, with :
- the letter from your newspaper/agency, stating your exact job, the dates of your stay. It can also mention what themes you’re working on.
- A couple of ID pictures (there’s a photo shop on the same side of the street, a block further)
- Press card
It takes a couple of hours to a full day. I don’t remember exactly, but it isn’t very long, and it was even shorter the second time I went there.
I don’t remember saying to the airport security I was a journalist, and I still got my authorizations, even for south Lebanon. I never had troubles with my gear either (that was between october 2010 and may 2011, maybe things have changed)
For the Palestinian refugee camps, it depends, I think you’ll have to get army permission for the one near Sidon. As for Burj el Barajneh, Sabra and Chatila, no special permission required, it’s good if you have contacts inside.