William F. Smith was born on April 9, 1840, in Pennsylvania, to John and Sarah Smith. His father was a carpenter who owned $8,000 of real estate and $5,000 of personal property by 1860. The family eventually settled in Dover, Delaware, and by 1860, Smith was serving as an apprentice carpenter.
He enlisted in the Union army on May 22, 1861, and mustered in as a sergeant on Company D of the 1st Delaware Infantry later that day. The regiment helped protect the Philadelphia, Wilmington, and Baltimore Railroad. He mustered out in August 1861 when his 3-month term of enlistment expired, but he reenlisted in the same regiment soon afterward and mustered in as a captain in Company D. The regiment took part in the Battle of Antietam, the Battle of Fredericksburg, the Battle of Chancellorsville, the Battle of Gettysburg, the Overland Campaign, and the siege of Petersburg. He eventually earned a promotion to major.
He was wounded at Fredericksburg and Gettysburg, and he was severely sounded in the right leg during the siege of Petersburg. Surgeons amputated the limb, but he died on November 6, 1864.