I have always had a mild loathing for the term 'networking' - I just see it as a very Dave Brent-esque term - but there is little doubt that it is important in any industry. Often the difference between those poker writers that find work and those that don't is simply being on other people's radar.
It is a tremendously easy time to contact anyone in the poker media, most people have a facebook or twitter account, or a website with a 'contact' page, with which they are happy to receive messages. Poker is not a world where the six degrees of separation rule applies, I would actually say it is closer to two or three degrees. If I am trying to contact someone, it is rare I don't know someone who knows them, and the chances are you probably have a better network than you think.
But first and foremost, try and contact people from their twitter/facebook/blog/website - the arenas where they have given their permission to do so.
The benefits of networking are enormous. Networking will get you work offers, interviews, invites to events, exclusive stories, and much more. Also, having a prior history with someone gives you an edge, a context, for working with them in the future. I recall I approached PokerNews several times trying to get work, but it wasn't until I met the then-editor Paul Sandells at a poker tournament that my (constant) attempts to secure work bore fruit.
Which brings me onto an obvious, but ignored, piece of advice - get out of the house. Get yourself down to the big events, get to your local casino, go to Vegas if you are thinking about going anyway. Meeting people in person is so much more effective. It can be very easy to think you can do it all from the comfort of your PC, but real life meetings are the best ways to leave a lasting impression. In the poker media, it gives you credibility.
That doesn't mean you should spend a fortune travelling the globe to get to these events, but you should definitely go to the ones nearby. There will always be something happening in your area at some point. I didn't go to Cannes for the WSOPE, but I always went when it was in London, and always venture out to EPT London - you just can't pass up great poker writing opportunities like that when they land on your doorstep.
Who to network with? Everyone. There is no right and wrong, and you certainly should not assume that the best opportunities come from the people highest up. Most of my most reliable contacts in the poker media are not the big bosses, they are the guys doing the work on the ground floor who actually have the time to talk to you.
One group to certainly mix with are the PR people and the agents. Be warned, more often than not they are trying to get you to write about something they are promoting, but what that also leads to is exclusive news and interviews. They usually have access to poker rooms, events, and top players. As long as you have your bullshit detectors ready and working, you will find them very helpful.
Finally, get active on poker forums and twitter. Not only is this a good way of being involved in all the major discussions and meet people, it is a great way to put yourself on the map as a poker writer. I can't tell you the amount of times I have had people introduce themselves to me in poker rooms by saying 'hey, you're DaveShoelace on the Blondepoker forum' - many of whom have gone on to become good friends or contacts.