How do I find a collaborator for a social science research project if I'm not in school? For context: I know exactly the topic and have an idea for the methods. I have done background research and seen what similar research has been done (and how). I have an associate’s degree. I live in Boston where I feel confident there must be some professor or postdoc or grad student who understands the details of the scientific method and academic publishing around here, but I am not in their social circle.

For now, I am mostly looking for someone to at least look over my methods and critique how scientifically sound they are (or perhaps propose better methods). Ideally they would also help me to publish this in an academic journal and offer some guidance as I conduct the project.

I will be doing this research either way as it is about an important social issue. I will be sharing the results with (hopefully) in news media, with (small grassroots) advocacy organizations I work with, and with local legislators. I figure, if I’m doing it either way, it would be best to have the institutional backing of academia. But I don’t really know anyone, so how?
There are a lot of universities in and near Boston. They all have websites and the websites usually include lists of faculty and their specialties. Find someone that way and write to them with a proposal and offer to meet with them personally at their convenience. Introduce yourself and give a bit about your ideas, but don't make it too long. 

Even if they don't want to work directly with you, many would be willing to give you advice about how to proceed once they know what your interests are. The larger institutions, with grad students, may even have a way for you to work with one of them. But academics are good at giving advice if nothing else. 

But, your proposal will need to be pretty compelling, since such people are pretty busy with their normal tasks. Some people will just ignore you for that reason. Keep trying.