The direction the track is laid does not affect the AI drivers. This is an urban myth according to the N3V developers. Track directions, however, will affect the direction of track objects and trains when placed, so it's best to lay the track in the direction of travel. It really does save a lot of time when placing objects as there is less fiddling to do with the track marks.
Trainz has always favored left-hand running. This was something the developers chose due to obvious cultural reasons. To get around this there are direction-specific track marks called direction markers to force the AI to take that particular track. They work like one-way signs and prevent the AI from taking the wrong track and force them to remain on the side you want them to.
In addition to the direction marks, there are also signals which will force the driver to take a right or a left. Their designation is something like Signal 06 RD, or Signal 06 Left RD. This means it's a type 06 signal that is set up so the trains are forced to take the right hand track. The Left in the name means it's a left-side signal.
You may want to look at the tutorial hear on signals and track laying. These are a bit dated, meaning written around an earlier version of Trainz, however, the concepts are the same and haven't changed much and are just as valid today as when they were written. Again, ignore the myth regarding track direction.
http://trains.0catch.com/tutorial.html
We say that there is a right or wrong side of the route for trains to run on. Keep in mind that in modern railroading, especially one that employs CTC, there is no such thing. A train can switch sides at any time to get around slower traffic or to get out of the way of faster trains. There are some railroads, though, in the US where predominant right-hand running is more common, that ran wrong main as it was called. One of them that comes to mind is the old Chicago and Northwestern, now a portion of the UP.
John