Make sure you go to New Scenario and select Tutorial if you've never played a Railroad Tycoon game before.
After the Tutorial, try out the Sandbox mode to get a feel for building railroads. This mode is fun, because it doesn't have the restrictions of finances.
Once you have the feel of the controls, try out the Campaign mode, going in order (the first few are easy).
If you're not into the heavy financial aspect of the game, but still want to play at a realistic level, assign a chairman to oversee finances while you focus on building and maintaining the railroads.