Networking is not just an in person activity anymore. You can network online (and be aware of your online presence, because that is another way that future employers and colleagues can judge you). Linked In is a great way to connect with current students during and after law school. You can also check out this previous post for more information about Linked In.
You can also join Linked In groups of your law school or undergraduate university to connect with others who share your collegial affiliation. Use those connections to your advantage as your network during law school and after you graduate. I use it now to connect to hundreds of alumni and former co-workers.
You can also ask your supervisor and colleagues to recommend you.
Lastly, you can search for jobs or ask those in your network to connect you with people in their network. You might use these networks to set up informational interviews to learn more about the firm or organization that you want to work in. More information about preparing for an information interview can be found here. During an informational interview, you are interviewing the person and getting more information about their work and the organization you work for. Feel free to bring the questions with you, as well as, a copy of your resume and personal business cards.
I also agree with the advice given on the career website mentioned above. Ask the person you are interviewing if there are others that they suggest you talk to and ask if they mind you using their name when you contact that person. I did that numerous times when I was in law school. But you don't have to be a law student to do an informational interview. If you are thinking about transitioning into another career or area, it might be a good idea to do a couple of informational interviews to see if that is someplace you might want to work.