Final Fantasy VII - Train of Corel
Solution 1:
To Stop the Train (and get the Huge Materia and Ultima Materia)
You only need to input 3 button combinations. The proper combinations, in order, are:
Up + Triangle, Down + X, Down + X.
To Get onto the Second Train
If you are having trouble speeding up the first train in order to catch the second, you simply have to alternate pressing Up and Triangle. So, press Up, Triangle, Up, Triangle, Up, Triangle, etc.
If you want more complete details on the possible outcomes on the train, go here and search for this text "{32} The Huge Materia: Corel and Fort Condor"
Solution 2:
There is a 'proper' way to do this but oddly enough there's another (easier) way.
It's been a while since I've played but you choose the option to speed the train up. On the third time of speeding up it cuts to the CGI scene and stops.
Sorry I can't tell you exactly what buttons but as I remember it there is a prompt telling you how to stop the train. Deliberately don't follow those instruction so that each time the train gets faster.
Edit: I found a clip which shows the process
Solution 3:
I have played FF7 many years ago, but I don't remember that I have big problem with Corel Train.
Looking through different forums and walk-troughs some people suggested to not follow the indications of buttons to quickly but instead suggest to take time and do them slowly.