Answer:
We use Lorentz-Drude formalism to represent metals, the software comes with most useful metals already defined (gold, silver, copper etc). You can find a simple example here:
https://optiwave.com/applications/fdtd-surface-plasmon/
You can also characterize materials as Lorentz dispersive and Drude dispersive. For details on how these materials are modelled read the Material Models section in the OptiFDTD Technical Background.