Learn English – “To steal the show” origin

The earliest use of it in print that I can find is from The New Monthly Magazine and Literary Journal, 1833. It is from a "paper" titled "The Story of Hester Malpas," by L.E.L.:

Hester now looked at her aunt, who was the very reverse of what she had imagined : she had always thought she would be like her father, and fancied a tall, dark, and handsome face.

According to an excellent post found at Wordwizard.com, and as seen in the citation above, the phrase was originally used to describe women as well as men up until the early 20th century (see EL&U discussion here). Also of note, the popularity of the phrase spiked after a movie by the same name was made in 1941 starring Caesar Romero.

The phrase originated in ancient Greece, as the moral of Hercules and the Waggoner, one of Aesop's fables.

A Waggoner was once driving a heavy load along a very muddy way. At last he came to a part of the road where the wheels sank half-way into the mire, and the more the horses pulled, the deeper sank the wheels. So the Waggoner threw down his whip, and knelt down and prayed to Hercules the Strong.

"O Hercules, help me in this my hour of distress," quoth he.

But Hercules appeared to him, and said:

"Tut, man, don't sprawl there. Get up and put your shoulder to the wheel."

Moral of Aesops Fable: The gods help them that help themselves

However, it is often mistakenly attributed to Benjamin Franklin or believed to have biblical origin.