You can't have more than one train running on the same track; the solution is to build a second (or third or...) track next to it for another train.
However you don't need parallel tracks along the whole way: with the use of traffic lights you can create a sort of passing place.
For example visit
http://home.c2i.net/cecilieTT/begicorn.htm#railwa and scroll down to "railways first". There you'll see 2 images of combinations of single and parallel tracks (it's hard to explain it in words).
http://www.railserve.com/jump/jump.cgi?ID=10957 features some more images and explanation of railway building.
The computer itself also uses this mix of single and parallel tracks, but don't take its way of trackbuilding as a good example... Those tracks will often include unnecessary curves, bridges, etc.