A lot of networking can really just be thought of as making work-related friends; Go to Computer Science based conventions, meetups, clubs, etc, meet people and be social! Talk about your work, make friends in CS, and work with those friends on projects. LinkedIn is great though, and you should ideally post somewhat often about what you're doing in related to your work/projects - Employers (from what I know!) like to look on LinkedIn to see what you're currently doing, and it's nice to see someone is avid on their work, posting about it regularly.
As for your school not organizing career fairs, I'd highly recommend you speak to someone about it. Often, a lot of networking doesn't happen simply because no one wants to be the first to "do it", even though everyone wants it. Ask your teachers about work experience opportunities that they're aware of, ask the school to organize career fairs, and get involved as a student "to be remembered", if that makes sense? You want to be the first thought/reference when someone needs a work experience over the summer, and schools tend to be subscribed to a lot of newsletters which publish work experience opportunities. Go out and ask all your teachers every now and then if they've got any new updates on opportunities, because they probably do. Always follow up on opportunities!! Never let teachers forget!!
I hope this is useful, this is just what I know from looking at networking in my own time, and what works from my attempts. Good luck!!!