Thanks to Thierry Depaulis for information on the history of this game.
This casino gambling game originated in France in the late 17th century, where it was known as Pharaon (first recorded 1688), and became extremely fashionable in Europe in the 18th century. After 1820, Pharaoh (Pharo, Faro) disappeared from Western Europe but became extremely popular in America during the Gold Rush, but is rarely played nowadays. It became a casino game when Nevada legalised gambling in 1931, but went out of fashion in the 1950s. The last faro "bank" was closed in 1975 in Ely, Nevada, although there was a short revival at Reno in 1980-85.
The betting layout consists of a suit of cards, from Ace up to King. Players bet on the card rank of their choice. The dealer exposes cards in pairs, a winner and a loser, and pays out or collects accordingly.
Faro was a derivation of Bassetta, which was introduced in Paris in 1672 by the Venetian ambassador and which can be traced back to the 15th century in Italy. Wikipedia has a description of Basset.
Detailed rules can be found on this archive copy of The Games Forum's Faro page.
There is another description of Faro on this archive copy of the Bicycle Playing-Cards (US Playing-Card Company) web site.
You can try playing Faro on line at the free Wichita Faro site.
Alpha Innovation has released a Wild West Faro app for Android, iOS and Amazon.