Landing a job as a product designer is as much about who you know as what you know. Networking can be painful, but it is a necessary step in your journey. Applying for jobs online often feels like sending your resume into the void, and knowing somebody on the inside boosts your prospects considerably.
For introverts, the best way to network is face-to-face with industry leaders or senior designers at companies you admire. There are numerous platforms to find such designers: ADP List, Behance, Cargo, Dribble, Medium, Slideshare, Twitter, and YouTube. These platforms are also an excellent means of discovering new designers - by following designers that other designers follow.
The best way to reach out is via direct email or LinkedIn. Be concise: include a sentence or two about who you are and a sentence or two about what you want to discuss. To be clear, you are not looking for a job; you are expanding your network and using conversations to grow. It is challenging to grow comfortable reaching out to strangers, but try not to take rejection personally. Many designers ignore such communication, but others will respond if and when they can do so.
If you can meet with somebody face-to-face - in person or over Zoom - come prepared. Refrain from wasting their time. Ask about their design journey and advice on succeeding in the industry. Use the opportunity to get feedback on your resume or portfolio. Thank them for the time and follow up afterward with another email. Meeting people in this way will build your network but also sharpen your communication skills and prepare you for job interviews.
If you want to get out of the house, networking opportunities are available at conferences, hackathons, and meetups. These tend to be even more awkward than cold communication unless you already know somebody. For the extroverts, though, they can be a brilliant way to meet new people with a promise to follow up in person.