Finding Research Papers

Google Scholar will automatically let you know if you can get access to the paper directly from the computer you're using. After that there is going to a library (they often have subscriptions to at least some journals) and visiting author websites.

Also, if you already know which papers you need, you can always ask here on LW

Ask on r/scholar on reddit. All my requests have been filled very fast.

Luke has some advice in this regard.

In addition to going directly to articles, consider dropping an email or two to researchers working on those topics (perhaps once you've found an interesting article of theirs). Many are very willing to provide their overview of the area and point you to interesting resources. While there are times when you won't get a response (for example, before conference season or at the end of the semester), most are genuinely pleased to be contacted by people interested in the topics they care about.

If you're looking for articles in the life sciences check out: http://www.hubmed.org

For physics and math check out: http://arxiv.org

If you were looking for articles in ACM or IEEE's digital libraries you could maybe direct-message a sympathetic LessWronger who pays for subscriptions and is willing to slightly bend copyright law and send you a copy. There's bound to be at least one.

I second the recommendation for Google Scholar, it indexes multiple versions of each paper and these often include freely available PDFs.