As the commenter above mentioned most of the major newspapers from that era will only be available through a paid database subscription. But you may want to see if your local public library has access to any. Most community colleges and universities will have access as well, but you will have to check with library staff to see what community members have access to. Talk to the reference librarians, they are to help. (I speak from experience. I work for two community colleges, reference librarian at one and the archivist at the other)
Most major newspaper databases (New York Times etc) in the long dark ages between 1923 and when newspapers commonly started publishing online in the 2000s are unfortunately paid subscription products.
However, if you're open to non-major newspapers, there's lots of good newspaper resources online. Check out:
Colorado Historic Newspapers Collection
Many college student papers are also digitized and online, they would probably have some neat student commentary/activism about smoking.
Many of those state collections I linked above also include the major college student papers for their state.
If you give me a more specific geographical interest I can probably find you some free papers for that area.
Good luck with your paper. :)
Go talk to your local library, I'm confident they'll have the know-how and resources (ie subscriptions) to set you up with what you need.
Your school board probably has a partnership that gives you access to your local university's library. Even if they don't, go to your local university, speak to one of the librarians and tell them what you need. In my experience, the librarians will get you setup and even assist in some of the research.