Join LinkedIn groups that interest you
. Send notes to people in your area who are members of your group(s) and ask them to connect with you (tell them you are looking to network in your area, and see they are successful in their field so you'd like to learn from them). Once they have connected to you, you have their email address about 95% of the time. Then email them and ask to have a networking coffee for 20 minutes some time in the next couple of weeks. Let them pick the place or suggest one (Starbucks is the old standby). For the meeting, don't bring a resume. Bring business cards if you have them or just paper and a pen and talk about the field you're trying to get into or the company you're trying to get into or however (and why ever) you connected with them in the first place. Ask for advice and take notes, even if it's something you've heard a thousand times before. Offer to buy the coffee. Ask if there are any books or blogs you should read, periodicals you can pick up, events you can attend, or groups (either virtual or in person) you can join that will help you along. Send an email thank you when you get back home. Keep in touch with them about once every 6 weeks or so, even if it's just to say hi or send a link to an article you saw that they might find interesting.
Some people will be helpful, some won't. But most people really, really want to try because they know exactly what it's like to try to network. Very often, it's the people who you think are least likely to be helpful who prove to be most helpful.
I've been doing this for a few months (I'm trying to break into a new field, so I need to start from ground zero and meet as many people as possible). If I write to 10 people to ask them to connect with me, I generally get about 8 yeses. Of those 8, usually 1 or 2 agree to meet with me. Of the ones who meet with me, about 1/3 - 1/2 have something helpful to tell me -- books to read, people I should connect with, blogs I should read, networking events to attend, companies that might be hiring someone like me in the near future, networking groups to join, etc. Plus every single one of these activities counts for job search activities (I don't know if you're unemployed and need to prove due diligence to Mass. Dep't of Employment and Training, but I am, and all of this stuff counts).
Also, I try to meet as much of a variety of people as possible because I'm trying to attack my problem (which is to become employed again) from as many different angles as possible. Hence I've now got a stack of books I'm going through, advice about business card design, brainstorming about who to approach and offer my services to, how to get started with blogging and even just some commiseration about how tough it is to find work these days.
Hope this helps!