Some of the best networkers I know seem to do it effortlessly. One of the keys to their success is to invert the exercise entirely. The best way to “network” is to approach it as an exercise of adding value vs one of extracting value.
In simpler terms, just be helpful, and don’t seek immediate outcomes from your connections. True network value will be realized in the long term.
This can happen a number of ways - my favourite is to imagine yourself as a colleague to whomever you’re talking to. This colleague that is vested in the success of that person will go above and beyond to help solve someone with whatever challenges they’re facing. It helps to take initiative by offering solutions, feedback or advice for a given situation. It helps even more if you open up your own network to that individual - and any time you can volunteer towards their problems will pay back indirectly in the future.
Essentially - be additive to your network, and it will ultimately be the same to you.