I've already linked to the documents that tell you how to configure multiple instances of squid in a cache hierarchy.
As for client configuration, if you have only one DNS server, DNS redirection is out. Manual configuration would be straightforward but possibly laborious, depending on the number of clients.
Alternatively, you could create Proxy Autoconfiguration files (
PAC files) that could automatically select the nearest proxy server. The PAC file could either be copied to each client and the web browser configured manually, or it could be served automatically using the
WPAD mechanism.
You now know everything you need to get started.