JSTOR is a database of journals, mostly from the humanities and social sciences. You can usually access it through computer terminals at libraries that have subscriptions, like your local university or possibly a city or county library (this would be more likely at the main branch of a library in a big city rather than the library of small town, USA). I believe that you can search JSTOR without a subscription, but you can't see the articles from the search, just titles and abstracts. You also should be able to get JSTOR hits via Google Scholar, while searching other databases as well.

Make yourself an account on academia.edu. It's like facebook for academics. You can list your research interests (and be as specific or vague as you want!), and the website will populate a newsfeed for you of papers people have uploaded. These include mostly conference papers, chapters for books, and journal articles.

When you find a few scholars you're interested in, or who seem to be interested in the same things as you, you can follow them, and the things they read and the people they follow will start popping up in your newsfeed as well. It's not as comprehensive as JSTOR, but you can definitely find a lot of really interesting stuff on it.

And no worries if your own profile is effectively a blank. There's lots of toiling historians who would be encouraged to know that non-historians are interested enough in their work to look them and their research up. They wouldn't be uploading their work to academia.edu if they didn't want you reading it!

It's a database with acces to most academic journals, it does cost money however. Most of the time you get free acces if you are a student or work in academia.

As of last year many archives on JSTOR are free to the public, but needless to say a lot of the more reputable academic journals require a subscription.