[squid-users] Transparent proxy with Ubuntu 15.04 and Squid3

[Jake]

I have a Squid/Dansguardian proxy server that successfully works when
the client web browser is manually configured to use the proxy address:port.

What I want to do is configure a transparent proxy server, presuming I
wouldn't have to manually configure browsers.

My LAN environment diagram:
http://imgur.com/0MybmwE

This is a home network environment with a cable modem, wifi router,
client web browsers, and I have added the proxy server as a virtualized
VMware server.

For the proxy server I have two virtual network cards on the same subnet:
eth0 192.168.1.14 (gateway and the proxy address)
eth1 192.168.1.15

Is it possible the proxy server can intercept traffic from the clients,
when the clients have direct access to the internet router? I don't
understand how traffic is "intercepted" in this diagram.

Do I need to change something on the router?

How do I configure for proxy transparency?

I've read some configurations, but they were confusing, or out of date,
or specialized without much explanation.

Thanks,
Jake