You already know Reddit is a treasure trove of awesomely useful everyday advice. But on game day, check out the NFL Streams thread to find a regularly updating list of sites other users are successfully streaming on.
This one may be obvious, but when all else fails, the best thing to do is just start Googling around for free streams of the game you want to see. With enough sleuthing and patience, you’ll probably end up discovering something at least borderline watchable/questionably legal. There are a handful of mostly dependable sites that aggregate links to illegal streams for pretty much any game you’d want to watch. Protip: minimize any sidebar live chats on the screen to improve streaming quality, and keep in mind that they’re all fairly sketchy. You could get bounced off at any moment, and there’s no telling what potentially harmful and intrusive software you may expose your computer to, so stream cautiously and at your own risk.