I agree with Suki, you have to let them get it off their chest FIRST before you try and speak. I try to start at the beginning annd take them through it slowly and calmly, explaining any parts they don't understand. Never say 'I don't know,' as this will wind them up. Say 'I'd have to check, or explain why that thing can't be done, insurance reasons or airline policy etc.
*WRONG*
PAX: You've lost my bag....
AGENT: Oh f*** off....
*LESS WRONG*
PAX: You've lost my bag...
AGENT: I personally haven't lost anything of yours actually but fill out this form and we'll be in touch
*SAFE BET*
PAX: You've lost my bag...
AGENT: Oh I'm sorry that seems to be the case (no pun intendeed). Let me check to see if there were any bags left behind at (departure point). While I do that Sir, could I ask you to fill out this form with the details of your bag. (I guarantee there will be a Gucci watch and handbag, Prada shoes, an iPod, colour TV and/or medication or other extrodinarily valuable items that said pax believes will be covered by the Airline.)
The pax will ALSO tell you that they were not given their baggage receipts. This is more amusing when you can see them stuck to the ticket.
So to sum up, let them speak first, don't lose your temper with them and remember that they are under duress while travelling and you do this everyday. Make them feel confident in YOUR abilities to your JOB...