Given it's your router you should already know this, but if you wanted to pretend you had no knowledge of the networks logical addressing structure you could use one of the following methods to discover it:
- Do a scan of the appropriate network range using a command line host/port scanner such as nmap, unicornscan, etc. This can be defeated by packet filters (firewalls) on the scanned systems. You also have to know that the appropriate range is, which you can find via DHCP replies or via sniffing.
- Capture traffic on the network and check the source and destination addresses. This requires that each system sends or receives traffic on the network during the time which you are sniffing.
- Access the router and check its DHCP database. Requires that you can access the router. Not all machines with DHCP leases are necessarily currently active on the network.