Researching medical studies

You can read pubmed if you're a subscriber...
Once you ID the specific journal you want to read, more may be available by googling it--a psych mag v. jama v. NE JAM, for ex.

There are some open access journals: http://www.doaj.org/doaj?func=subject&cpid=20
Some other journals embargo recent issues but you can get access to older issues from their website.

I use pubmed a lot, so let me give you my best tips. SOME articles on pubmed are available for free, but you're right that the majority are not. This is how you access the free studies:

Go to pubmed and click on the tab labeled "limits." Select the little text box called "Links to free full text." Type in what you want to search in the search bar, "Parasites of south america" or whatever, scroll down to the BOTTOM of the page, and click the "Go" button (not the top go button!). Now all the studies that pop up will have links to the free full text in the abstracts. You can read them for free. Beyond that, yes, a university library can get you the non-free studies. Sometimes your public library can request photocopies of the studies from interlibrary loan through a university library, but YMMV there.