While not directly related to networking in particular - I would recommend giving your expertise away. Seriously.
I know that sounds odd, but when you give of yourself - this is how people get to know what you can do, and what you're capable of. What I'm suggesting is that you think of ways you can be of service or help in some way, just because. This will go a long way in terms of developing your own skill set while showcasing your talent and skills.
The best 'networking tip' I can think of is to donate your time and expertise - share your passion and help people. You do not have to wait to be paid to start doing your best work. It's actually even more satisying to give of yourself while you're waiting to get your career off the ground.
Don't wait around for contracts or for people to pay you for your expertise - give it away. That's the best advice I can suggest. When you do this, people get to know you, in a non-threatening and non-commercial way - they don't feel like they're going be asked for something, and yet - they are finding out just what you're capable of doing.
Does this make sense at all?
What is it that you're passionate about, and what are you really good at? Take that thing and give it away. Not because you're trying to drum up business, but because you love the work and because you have something to offer. Share (and give away) your gifts.
Look for ways you can help, without expecting anything in return - because you love the work you do. I honestly cannot think of a better way to 'market' yourself. Just get out there and start doing it. Offer up hope and help - and give gifts. Be there, in unexpected ways. Just show up and do your best work (paid or not) anyway.
