Networking as a writer has never been so easy with the rise to fame of social networking sites!

I recommend twitter for following all manner of writers (sign up and then search for "writer", "screenwriter", "poet" or what have you and a list of relevant profiles should appear).

Following fellow writers is not only inspirational but could lead to all sorts of opportunities, too. It's also worthwhile joining in with writing discussions or debates through twitter - you can learn a lot!

Another excellent tool for writers is facebook. Like twitter, it's easy to set up an account. Facebook's strengths lie in groups (writing groups, organisations, production companies etc) that you can join. You can also become a "fan" of films, TV shows and organisations. Groups and fan pages update regularly so it's an excellent way of keeping up-to-date with news and opportunities. 
 
Other Writing Social Networks
UKwriters social networking site
Peer Review Websites
Want to get your work critiqued for free? These community websites are an excellent way of getting advice and improving your work.

Peerage
Sharpshooter
A Screenwriter's Workshop
Forums
Forums are an excellent place to ask questions, share ideas, discuss related subjects and get friendly support from fellow writers.