Networking seems straightforward, but building meaningful relationships, like all things, requires practice. The more you do it, the better you become.
Start with the people who know you best. Tell your inner circle of your thoughts and intentions. See if they have any ideas or know of anyone you could speak with.
If you want to advance in your current position or make a parallel move, talk to your supervisor and get a sense of what is possible and what you would need to do.
Join a local alumni group from your alma mater. Attend events to see what others from your school are doing. The good news is that you already have something in common with these people.
Join the ones that are relevant to your work and interests. Attend meetings, "networking events," which all include pleasant wine and drinks, and begin introducing yourself.