Normally they require you go to a police station and get a police report. The reason for that is that you are now legally saying you lost your phone and can be prosecuted for theft by deception if you didn't and said you did.
They will send you your replacement refurbished phone (if they have them in stock) or a replacement new model phone (if they don't which is rare) when you contact them about a loss. Once the new unit arrives, it will come with all the instructions to send the old one back (even if lost or stolen - if you recover the device they ask you to send it back to them) along with a prepaid mailing label. Normally you just put the old unit (minus battery, battery cover, and anything else that didn't come with the new unit) back in the same box, seal the box, place the label over the old one (always recommended to remove the old label in case the new one comes off) and send it back to them.
Zo