Earlier quoted context omitted.
It's illegal to work for free today, unless you're a Congressional intern, since they exempted themselves from the law. Lots of "my grandfather..." stories are illegal in today's US, land of freedom and such.
In this case, you could still work for free, as a volunteer at a charity. Or attend user group meetings and give presentations. That is one way to increase your network.
You realize the article specifically highlighted that as one of the bad pieces of advice proffered on the Internet.