If both computers are connected to the same router then they are already networked. But if you don't know how to transfer the files directly (i.e. without going out over the Internet) then I suggest you just ICQ them. For just 50 photos it will take way less time than figuring out your LAN.
For the long run, though, I suggest you set up password-protected shared drives between the two computers. Then you can just drag and drop files from one to the other.
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