The search page for Google News Search Archive looks like this:
The search string I ended up using was [seaver family -tom -pains]. The "-tom" eliminates many of the articles about my cousin, Hall of Fame pitcher Tom Seaver, and the "-pains" eliminates many articles about the fictional Seaver family on the "Growing Pains" TV show from the 1980s.
Here is the top of the first page of the matches:
As you can see, there is a timeline across the top of the page which reflects the number of articles found in the search. A user can click on a year in the timeline and see the articles for that year.
Here is the bottom of the first page:
One article on this list caught my eye - "Family Trees Yield Big Coin" about a genealogist who had a genealogy scam selling family history books, Jesse Montgomery Seaver. I clicked on the link and saw the article in the Spokane (WA) Daily Chronicle dated March 20, 1934:
Some of the articles found by Google News Archive Search are free to access, as the Spokane article above was. Some cost money to view and download - it depends on the newspaper company that Google has an agreement with.
I look at this as another newspaper resource - the free articles are wonderful, and the paid ones provide leads for the researcher. The researcher needs to decide if they want to pay the online fee for the convenience of having the information now, or note the source and try to find it using a local library or researcher, or other online resources.