How did Gerald Ford become president without an election?

In 1974, President Richard Nixon resigned from office due to the Watergate scandal. His vice president, Gerald Ford, automatically took over under the terms of article 2, section 1, clause 6 of the 25th Amendment to the Constitution. This clause states unequivocally that, in the event of an incumbent's dying, resigning, or being removed from office, the vice president is the immediate successor. As Ford was Nixon's vice president, he became the 38th president of the United States on the same day that Nixon resigned from office: August 9th, 1974.
Unfortunately for Ford, he was unable to pass his one and only electoral test. He lost the 1976 presidential election to Jimmy Carter, which means that he has gone down in history as the only US president never to have been elected to the office.