New, green and trying to get everything working

I have a hard-wired LAN at my home with several PC’s on it connecting through an old LINKSYS BEFSR41 4-port router. I don’t know anything much about all the technology and I should not, IMHO, need to. I just want to be able to see all the PC’s on my LAN again. I tried reading through many, many posts in several forums but all I got other than annoyed at the poor English language skills of many of the posters there, and glazed eyes, was nowhere.

One machine is running Vista, another has XP SP3 and the other is running Linux.

Please point me to the information I need.