There are 10 trains available during the 1890s. You start with 1 unlocked and need to research all of the others.
The actual trains have a total research value of 1600 points but you will need to also buy some of the other technologies (at least 900 points worth) to unlock them. All together you're looking at just over 5 years of research to unlock all trains. Some time can be saved by building universities (they earn extra research points) or by winning technology in auctions.
This achievement is fairly easily earned during the South Scenario which takes place in the 1890s. If you complete the scenario before you unlock the last train then pick the option to keep playing, it shouldn't take long.