Nearly every paper written since the mid 1900's can be found online at these two sites:
ArXiv - You can think of this as the daily astronomy newspaper. Each day, papers are submitted and posted to the ArXiv, where they are available to be read for free (as in you can read them anywhere and don't need access from a university journal subscription). Not all of the papers on here are peer reviewed, but most are. You should get in the habit of perusing ArXiv each morning to get a sense of the new science being done across astronomy, not just in you field.
ADS - The Astrophysics Data System is a convenient tool that allows you to query a large database of astronomy papers. You can give ADS an author name (or multiple), range of years to search, keywords, or even a title, and ADS will return a list of papers that match your criteria. The ADS results contain links to abstracts, full articles, data products, and bibliography information. (Pro Tip: If you are searching for the first author of a paper, put a carat before the name. Example: ^Casey, C)
Tips and tricks for getting the most out of scientific papers:
- "How to (seriously) read a scientific paper" - Elisabeth Pain (Science Magazine)
- A guide to reading papers from Astrobites
- Tools (part 1 and part 2) for reading papers from Astrobites