There is a fuse for the horn ~ believe it's in the battery compartment bit with the fuses in there (15amp). That would be my first idea to check.
Otherwise it might be a lose wire in the steering wheel, faulty ground or (unlikely) both horns have simultaneously failed.
After you have checked the fuse & if it's ok then here's a guide on how to get at the horn wires inside the steering wheel; http://www.350z-uk.com/topic/32500-how-to-remove-the-steering-wheel/
Some more related threads; http://www.350z-uk.com/topic/83771-steering-wheel-horn-faultybroken/
http://www.350z-uk.com/topic/42823-horn-wont-work-fuse-is-fine/
http://my350z.com/forum/maintenance-and-repair/240982-horn.html
Hope that helps a little.