We knew that Thomas Kowalski was born in Poland sometime around 1875 and that when he came to the United States he first lived in Pennsylvania and then later Ohio where he worked for a steel company.
We first tried a Google search for "Thomas Kowalski" Pennsylvania and then for "Thomas Kowalski" Ohio but nothing in the results was helpful. So we searched the US Federal Census where we found a number of Thomas Kowalskis but there wasn't enough information in any records to indicate that we had found the Thomas Kowalski we were looking for.
So we went to the Card Catalogue at Ancestry.com where we searched some of the collections. Here we found a copy of the US World War II Draft Registration Card (completed in 1942) for Thomas Kowalski. It indicates that he was born in Poland on December 22, 1877. At the time he completed the draft registration card he was living in Portsmouth, Ohio and working for Wheeling Steel Corporation.
Next we did another Google search and entered "Thomas Kowalski" Ohio Wheeling Steel. One result was a link to an obituary that was posted on the Kowalski Family Genealogy Forum at Genealogy.com.
The obituary indicates that Thomas Kowalski was born in Poland in 1877, became an American citizen in 1948 and died on May 21, 1960. He was survived by his his wife, Anna Marie, daughters, Mrs. Stella Hoberg and Mrs. Julia Ohda, sons, Joseph and Chester, a brother Lewis, 12 grandchildren and 3 great grandchildren.
In some cases you might know an ancestor's death date but the obituary is not online and you don't have access to a library in the area where your ancestor died.
Look online for a local genealogy society or genealogy group in the area where a newspaper might have published the obituary. The genealogy society or group might have volunteers who will look for the obituary at no charge or for a nominal fee. The local library might also have procedures for obtaining obituaries for people who do not live in the area of the library.