The first dial telephone was introduced in 1897 by the Automatic Electric Company, founded in 1891 by Alman Brown Strowger, a Kansas undertaker. In 1889, convinced that the Bell "central exchange" was diverting his incoming calls to a rival embalmer, Strowger invented the automatic switchboard system, which was controlled by a number-dialing system. The system was first installed in 1892 in LaPorte, IN. In Strowger's 1897 model telephone, however, the rotary dial had not holes, but depressions similar to gear teeth, along about 170 degrees of the edge of the dial disc.
The telephone, of course, was invented by Alexander Graham Bell (1847-1922) in 1876. The first commercial exchange was opened in 1878 (with 12 users), and in 1879, the multiple switchboard system was invented by engineer Leroy B. Firman, making the telephone a commercial success with 250,000 users by 1890.
Up until 1894, when Bell's original patents expired, Bell Telephone Company had a virtual monopoly on the market. They had brought successful infringement suits against at least 600 would-be competitors. The company had, in 1896, just introduced the "Common Battery" system, with a power source at a central exchange. Before that, one had to hand-crank the phone to provide enough power for a call. A connection could still only be made by giving the name of the person to be reached to a telephone operator. This is what Strowger changed.
Strowger soon became a strong competitor of Bell. He introduced a tabletop dial model in 1901, which was cleaner in design than the Bell model. In 1902, he introduced a wall telephone with a dial disk, this time with actual finger holes, but still only 170 degrees around the disk. By 1905, a "long distance" finger hole had been added. The last known Strowger model in in 1907. Strowger patents presumably expired in 1914, and he or his company is never heard from again. Not until 1919 did Bell introduce the dial system. When they did, the finger holes extended fully around the dial disc.
The Strowger-invented dialing system did not become common until 1922, when it reached large cities like New York. But once established as the norm, it remained the primary telephone technology until the 1970s. After "touch-tone" dialing was introduced in 1963, the original Strowger-invented finger-dial system became known as "rotary dialing." And that's how Strowger "let your fingers do the dialing."