The biggest misunderstanding
Most people think networking means handing out cards and pitching themselves. That fails almost every time. Good networking means being useful and building relationships before you need anything. It takes patience.
Choose where to spend your time
Only some events are worth your time. Pick groups, events or communities where your ideal clients or people who can refer you really meet. You get more from two good events that you visit again and again than from ten random events that you visit once.
Help others first
Go in with the question "who can I help here?". Introduce people to each other, share useful information and listen. Over time, people know you as a helpful person, and they think of you when an opportunity comes up.
Have a clear, simple introduction
When people ask what you do, answer in one specific line that they can remember. Skip the job title. Say which problem you solve and for whom. People can only refer you if they remember what you do.
Follow up, properly
You get most of the value from networking after the event. At the event, you only start the conversation. Within a few days, send a short, personal message about what you discussed. People respond far better to this than to a general LinkedIn request. Few people follow up well, so those who do are noticed.
Be patient
Networking is a slow channel. Someone you meet today may become a client in two years, or refer you in five. Going regularly over a long time is far more important than any single event.
Further reading
See also Raising Your Rate With Existing Clients, Keeping Clients and Earning Repeat Work and Acquisition for Starters.