Since I just was interviewed about this topic, I'll try to write down some of my recommendations on how to build a professional network if you are early in your career and how to progress from there. Actually I am practicing all of these actions even today.
I'll focus on building a network to other professionals in your industry, since this will enable you to learn about new technologies, improve you skills based on experiences they are sharing and ask for support, find mentors and later on jobs and hires.
In my experience the tech scene is especially good approachable on Twitter. I find myself following a lot developers there and this way I get daily access to what is going on tech-wise. The real-time character of the network has it's advantages: you can easily interact on a given topic but it rarely happens that someone resurrects a old post. It's very easy to approach someone with a question there, and they usually will answer right away.
But make now mistake, following someone on Twitter is a one-way street, to build a network you have to share something so people can become aware of you. And since connections are built on trust, it means you have to expose yourself to some degree. And this exposure needs to happen in the physical world, only there will you be able to build connections that support exchange about personal and confidential matters which is the basis for finding good advisors and mentors.
The first step is to go to local meetups. Do not fear to go there as a beginner, the first step to learning something is to embrace the unknown. It's a great opportunity to learn to know new people and find out who you would be interested to talk to. You will find that approaching someone there is a lot easier compared to a contacting them only e.g. through LinkedIn. Since you are both part of the same interest group, and you took the time to be present at the meetup will give you already some credibility. Also, it's harder to turn down someone who is approaching you face to face.
Early in your career you should develop the confidence to give your first talk. Watch other speakers and try to find someone with experience as a speaker to give you feedback on your talk. Most meetups will be happy to host a beginner talk, since they always provide really valuable input. Giving talks will put you in the spotlight—doing it at a small meetup where you know people can be even more uncomfortable compared to a huge conference—but it also gives you a lot of visibility. I can highly recommend the software crafter communities around the world as a very inclusive and beginner-friendly community of professionals.
Every talk creates the opportunity to reuse the content in multiple ways. You can use it to share your findings on your blog, but even better: submit it to a conference.
The next step of building a valuable network is to attend conferences. At conferences you will be able connect with a great variety of people. Those that share the same problems as you do and other beginners which will be a great resource when learning a new topic since you can exchange about your findings and problems. Since last year, it became common to connect through a Slack instance for that conference. Here you can also easily approach speakers, with your questions or on general to just give them feedback on their talk. In both case they will usually be very open and happy to help you. It's a good idea to check out a conference schedule beforehand and follow the speakers on Twitter, doing that you can start building a connection to them even before the event.
You should submit your beginner talk to conferences, because giving a talk will teach you so many great things that improve your skills on many levels. You can find conferences that accept proposals (Call for Papers, or CfP for short) on papercall.io or through lanyrd. Karolina has a great post on How to write a successful conference proposal. Becoming a speaker on a conference will give you a lot of visibility and provides a great opportunity to meet other industry experts on eye-level.