I suggest that you get comfortable. When I quit my job at a top firm in Boston to move to New York to be with my fiancé (now husband), I had no idea how to network and, had I known, I would have been anything but comfortable! The good news is that by the end of the process I was so comfortable that I was actually making lunch dates with my fiancé's partner's ex-wife's new husband (who was a partner at a top New York firm). The new husband was a great guy who took me out for sushi a couple times and provided many valuable leads.
Where do you begin? You begin by creating a list of all the firms that interest you and then targeting alumni from your college and law school who are partners at said firms. How do you "target" these partners? You write letters to them (real letters on bond paper not emails) and you close those letters by indicating that you will be calling to arrange an
"informational" meeting. Once your targets know that you are not expecting them to give you a job, you have let them off the hook and they are more likely to meet with you. The meeting is your opportunity to impress these potential employers with your abilities and drive. It is also an opportunity to demonstrate that you would be an outstanding employee. Your targets may not be able to offer you a job today, but if you impress them at your meeting, they will remember you when they are hiring, or they may recommend you to a colleague who is hiring. The latter is what happened to me. The new husband remembered that I was looking and he recommended me to a colleague. Through that recommendation I ended up working at Paul Hastings!
Furthermore, you should talk about the fact that you are "in the market" at every opportunity with every person who is willing to listen to you! The new husband was not a contact I made via the above referenced approach of targeting alumni from my college and law school (though said approach did yield many meetings and certainly would have led to a job eventually.) Rather, my meeting with him was a product of the fact that I made a conscious effort to market myself at every available opportunity. If you truly force yourself out of your comfort zone (which is so important in every aspect of your life) and actively "network" (no matter how "uncomfortable" you may feel initially), I guarantee that you will be pleasantly surprised by where your efforts lead you!