How does one get started as an English proofreader in Poland?
Other people have mentioned some of the practical networking stuff, I'll mention...
The best tactic is to not need to support yourself economically right away. Living in a new country (even one you've visited some) is very different from the long haul and it takes at least a year to learn how things work - the less stress you are to find work during that necessary period of adaptation the better. NB! The less time you think you'll need to adapt the more time you'll probably actually need.
Second, polish your Polish! Ironically, the better your Polish the more work will come your way. More than once when I have gone to meet a potential client they've been nervous and awkward until they realize I speak Polish (a signal that I know how things work and won't burden them with weird foreigner requests) you can sometimes feel their tension dissipate...
Be clear about what you can and can't do. If it's not a field you're familiar with explain that and explain that you might not recognize jargon (or technical terms) in the field and that someone who does know that should check your work out. Professionals often (not always) know this, but you need to be able to explain it.
Make sure your English is up to snuff. Just being a native speaker isn't enough, you need to have a solid grasp of different registers (informal, neutral, formal, general, academic etc) and you need to be willing to look up stuff to back up your changes (many people are liable to second guess or undo your changes if you can't defend them).
Be assertive, Poland is no country for people pleasers... don't be rude (a delicate balance for anglophone people) but if you don't learn to be assertive you'll end up with footprints on your forehead.