Sometimes the simplest is not so simple!
Around the world, the name "straight rail" is not used to describe the basic carom (ball to ball) game. It is generally called either the free game, which is the English translation of the French "partie libre," or simply "libre." In America, we still call the basic carom game "straight rail" even after triangular balk zones in the corners were introduced limiting the number of points a player could be scored in those zones. These zones gave birth to the "championship game," where the corner triangular balk was extended, moving it to the first diamond on the short rail and the second diamond on the long rail.
The game played in the tournaments in Europe and elsewhere is the championship game, where the number of points in the corner zone is limited much like in a balkline game. But for beginners, or even for seasoned players in America, drawing the championship balk is not necessary for competition as the quality of play will not rise to the championship level.
Without competition, endless hours of enjoyment can be had by practicing gathers and the various nurses. The entire purpose of straight rail is to control all three balls and get them in a position where ball-to-ball scoring is made easier. The gather shots ("rappels")are designed to move the balls into a controllable position, typically by driving the first object ball one or more cushions in a manner that it returns at or near the point where the cue ball scores softly in a carom on the second object ball. A nurse is a technique employed when all three balls are extremely close together especially near a rail. Properly employed it enables points to be scored without losing the position of the balls. There are various nurses, but the most famous of all (and the one that destroyed the game for spectators) is the rail nurse, which is known to the world as the Série Américaine because American players perfected it. The rail nurse moves down the rails with the player replicating the position of the three balls after each shot. It is endlessly enjoyable trying to score in the rail nurse, but it's not as easy as it seems. Just try it. Make 10 or 20 and you've accomplished something. Of course, the pros became so efficient at the rail nurse that they were able to score thousands or tens of thousands points without losing the position! And players like Caudron don't worry when they lose the nurse position; they just recall the temporary lapse of memory of the errant balls by executing a drive that gathers them back into position – a joy to behold.
An excellent book on straight rail is Maurice Daly's Daley's Billiard Book, which has been re-printed many times since it first appeared in 1913. It can still be found in paperback for $15.00.
For some diagrams, see http://biljarten.gobase.info/Study/livres/americain/index.phtml.
Also essential in playing, or practicing, the free game is learning the various gather patterns. A good start (and perhaps the only source you need to consult) is Weingartner's billiard program, developed by Heinrich Weingartner. It has 76 practice gathers. For an online version, go to http://wbpb.blogspot.com. (You need to have Abode Shockwave to see the diagrams.)
And finally enjoy some great instruciton videos we have assembled for you in our Straight Rail Video Gallery.