What follows are specific to finding and reading the kinds of stuff that I actually find and read professionally. So, generally falling into the medical, social and informational sciences. There are certainly better resources for other domains, like Physics and Literary Criticism.
Far and away the most useful thing to do is find someone who knows a lot about the discipline you're interested in. Ask them for some core references. Ideally, they have a reference management system that they share on-line, like Zotero.
Zotero is currently best used via a plug-in for firefox. You can read all about installing and using this plugin (including a video) on the Zotero site.
Sadly, that link doesn't say much about the cool social and syncing features (that you need to use to access group libraries, for example). So, looked at the previous link to get your bearings and install the zotero plugin as instructed. Now, if you haven't done so already, you'll need to make an account. In the middle cluster of buttons in the Zotero interface, you'll see one with a gear on it. Click, then select "Preferences..." At the top, you'll see a "Sync" icon, which will open a page with a link that says "Create Account." Click that and do it! Then return to that same "Preferences..."->"Sync" window and enter your new login information. Once you do this, any groups you join will show up magically in your browser, including the papers!
Then, if you need to find stuff on your own, the two best (public) resources are probably PubMed and Google Scholar.