My first tip is to simply be yourself. I’m at my most comfortable when I’m being informal, and when I’m able to chat to people about things other than work! Don’t try to force yourself to network in a way that feels uncomfortable to you: if big corporate events seem insincere, avoid them. If all your colleagues are encouraging you to mass-email “useful contacts”, go for a personal and authentic approach that suits you, instead.
Networking doesn’t have to be a cold, corporate activity. For me, good networking goes hand in hand with being a good friend. That means asking clients how they’re doing, and taking a genuine interest in their life and their concerns. People are much more likely to send repeat business to you if you’re their friend rather than just some random contact they once worked with.