From the default configuration, I make the following changes to my squid.conf file
http_port 0.0.0.0:3128
cache_dir null /tmp
(for non-caching proxy)
or
cache_dir ufs /squiddir 5300 16 256
(for caching proxy, use a separate disk spindle where possible, separate controller channel if available.)
acl our_networks src (My class C)/24 127.0.0.1
http_access allow our_networks
cache_mgr root
cache_effective_user squid
cache_effective_group squid
Start the squid service (as root: 'service squid start' on Fedora) and you should have a functional proxy (caching or non-caching, as you chose in your configuration file.
Be sure your firewall is blocking port 3128 from the public Internet, or you will be in for a big surprise.
Point your favorite browser at (your proxy's IP address) port 3128 (unless you chose a different port in your configuration) and you'll be ready to browse through the proxy.
Rather than opening up port 3128 to the public Internet, I would strongly suggest configuring an ssh tunnel from wherever you are back to your proxy.
For SSH.com Secure Shell, the settings are:
Listen Port: 3128
Destination Host: 127.0.0.1
(assuming that the box you are ssh'ing to is your proxy, otherwise specify the IP address of the proxy in as seen from the box you are SSH'ing to (usually the private, local network IP address) here.)
Destination Port: 3128
Allow Local Connections Only: Yes
Type: tcp
For PuTTY the settings are:
Source Port: 3128
Destination: 127.0.0.1:3128
(Select "Local" radio button)
Again, 127.0.0.1 assumes the box you are creating an SSH session to is the same box running the proxy. If they are two separate boxes, specify the IP address you would use to connect between box1 and box2 (probably your NAT'd local, private IP address.)
You can choose to use a hostname here, but be sure your ssh target box knows your proxy box by this DNS name for it to work. The DNS reference is between you ssh target and proxy, not necessarily the same reference as returned by a public DNS query on the Internet.
Connect an SSH session with the correct tunneling settings, point your browser's proxy settings to 127.0.0.1:3128 and you should be browsing through your proxy. Opera will show you this on the status line "Sending request to www.slashdot.org (your.proxy.ip.here)". Firefox doesn't seem to show this by default.
All you browser developers, I'm still waiting for a nice standard "Proxy On/Off button" to be built into a browser, default view, default installation. Opera had a nice check box feature that can be added to a tool bar. Works great, but I lost the URL to where to get it.