Rather an expensive proposition I'm afraid.
Essentially you need an Ethernet to Fiber media converter on each end of the fiber. These are not cheap. Low end ones run about $50 on ebay and will need to be powered from a wall outlet. (You need to know what type of fiber you have and make sure that the converter has the right connectors for your fiber) Then you will need some fiber cables to connect from the wall to the converter. (also not cheap.) If the router is not at the central distribution point for the fiber then you will need some sort of fiber patch system unless it already exists then you just need another pair of connections.
I think you need to just buy a good wireless modem and use WP/WPA2 encryption. Or maybe if the cables are run in plastic conduit you could just tie Cat5e wire to the fiber and pull it back through the conduit.
Argh, how can something - which must be a reasonably common request - be so inconvenient/expensive? It figures, though, since Google wasn't being of much help (hence why I posted on here).
I guess I'll have to do that, then.
Thanks a lot for the info, Ron!