Know why you want to network. Is it to raise your profile, create new opportunities, build alliances or simply to be well informed? When you are clear why you are networking then you are much more likely to do it well.
Be subtle. Great networkers are rarely considered as 'great networkers'. They are usually seen as interesting and interested.
Make sure that you are up to speed on current affairs. This will help you introduce new information (and so be interesting) and give the impression that you are on top of things. The same applies to what's going on in your business for internal networking.
Ask questions. People are generally more engaged when they are talking and being listened to rather than the other way around. This will also give you plenty of opportunities to spot mutual interests and so build rapport and deepen the relationship.
Do your research. Asking someone if they know a company well and being greeted with the reply, "I used to be their Chairman" is more than embarrassing.
When you introduce yourself, give more information than just your name, eg, "My name is Mark; I worked with Marianne on the merger", or whatever might help the other person continue the conversation and build a connection.
Hold off on asking your critical question (or favour) until you are confident that the relationship is good enough. If you have built rapport effectively and contributed something worthwhile to the conversation there will almost certainly be other chances.
Follow up. This is where supposedly 'natural' networkers fall down. Do whatever you committed to, send a follow-up e-mail, invite them to a suitable event, and refer back to the conversations that you have had.
Keep trying. The more you practise, the better at networking you are likely to become, and the easier it will become.
The knowledge economy is being replaced with the networked economy. If you want job security or a meteoric career, building effective networks is one of the best ways of getting them.