You can certainly try using the free Internet to find newspaper articles by searching Google, Bing or Yahoo - usually through an advanced search. However, most newspaper publishers expect payment to view the whole article.
Your library has subscription databases that house hundreds of thousands of newspaper articles. You have access to the entire newspaper article because your library pays for that acccess.
Using the library's subscription databases is the best, fastest and easiest way to find a newspaper article for your research.
If doing an internet search it is easiest to go straight to the newspaper's web page and search their site. Example newspapers would be: The Austin American Statesman, The Dallas Morning News, The Houston Chronicle, The New York Times, The Wall Street Journal, The Washington Post, etc.