Using arp should be pretty accurate as @ussnorway suggested. Basically everytime a device on the same LAN is trying to locate the gateway it will send out a broadcast query. Every system on the LAN will see this and add it to its own arp cache. You can also use a network scanner such as zenmap Zenmap - Official cross-platform Nmap Security Scanner GUI which also can identify open ports and OS fingerprinting to name a few things.
You can also login to each computer bring up a Command Prompt as in Norway Post #2, and type "ipconfig" <enter>. On my laptop here, it's current IP on this LAN is 192.168.0.11. The local Gateway of the Cable Modem is 192.168.0.1. As shown here:
Repeat this procedure on each computer connected to your LAN.
Using arp should be pretty accurate as @ussnorway suggested. Basically everytime a device on the same LAN is trying to locate the gateway it will send out a broadcast query. Every system on the LAN will see this and add it to its own arp cache. You can also use a network scanner such as zenmap Zenmap - Official cross-platform Nmap Security Scanner GUI which also can identify open ports and OS fingerprinting to name a few things.