I figured from squid tutorials that the simplest configuration to do this is:
http_access allow all
http_port 3128
coredump_dir /var/spool/squid3
refresh_pattern ^ftp: 1440 20% 10080
refresh_pattern ^gopher: 1440 0% 1440
refresh_pattern -i (/cgi-bin/|\?) 0 0% 0
refresh_pattern (Release|Packages(.gz)*)$ 0 20% 2880
refresh_pattern . 0 20% 4320
cache_peer 10.1.2.3 parent 80 0 no-query default login=my_username:my_password
never_direct allow all
These lines should get you a working proxy server on your local machine that forwards all requests to another proxy server (change ip addresses accordingly). However, please note that in the above script, I have disabled any access control/filters, so potentially, anybody can connect and use your proxy. You need to add additional code to restrict entry to only some devices.