Over on the Jobs in the Money blog, there's a link to an article on networking that recommends networking strategies for introverts. In addition to their recommendations, including attending professional and social events and volunteering for leadership roles in professional organizations, I have one more idea to add.
If working a room isn't your thing, a great way to gain a comfort level with networking is to take advantage of the ever-growing list of on-line networking tools. LinkedIn, Ecademy, and Ryze, just to name a few allow you to connect with members on-line. For introverts, this approach can be a great place to start a networking campaign. The beauty of the on-line world is that you can think about what you want to say and review and tweak your message before you hit send. (Who hasn't wished they could do this at one time or another in a face to face meeting!)
While on-line networking should not replace traditional networking opportunities, it is a great way to supplement your ongoing networking campaign and gain a comfort level with the process.