I got into contracting by applying for a contract in the SF Bay Area from Florida, did a phone interview,received an offer -- to contract at Hewlett-Packard. I believe I found the contract on dice.com, which also helped me find other contracts. I already had experience building software for my parents' company, and had built some of my own sites, including CGI stuff that I had to pay $125/month for a shared account for, back in those days! I didn't realize what my market rate should be on the first contract. I then got recruited away by a startup to help build the first online yellow pages site. HP asked to make a counter-offer but I (foolishly) didn't let them. After some time at the startup (which later turned down an acquisition offer from pre-IPO Yahoo, doh!, and finally basically shut down), I returned to contracting, this time to Schwab. Then I did some freelance, and then returned to help the same group at HP for a short-time. Then contracting at Bank of America. Then a short contract for a web dev shop, and then got into angel investing (Napster), and co-founding startups (social networking pioneer Ryze).
Now several startups later, I've returned to a combination of remote contracting and/or part-time co-founder (heard this term yesterday :). Some companies I've helped on a cash basis (hourly/weekly rate). In many cases, it is combination of cash plus equity. I'm just wrapping up a contract where I built out the server and dev-ops infrastructure and code for a new startup, as well as helping w/ analytics, product, etc. (and where I continue to be a senior adviser).
My experience has been that the on-site contracting market in the SF Bay Area is quite efficient and dynamic, and networking is not necessarily needed. Although I did a lot of networking in the early days, which has been great in opening up opportunities over the medium/long-term, the networking was not a factor in getting leads for on-site contracting. However, it led to some resume bullet points that may have been helpful in landing some of those contracts (e.g. landing the BofA contract was helped by my experience coding some of the first Java applet ads for Symantec back in the day that was a freelance project that came from networking).