Within a city, they will most likely have some type of fast track train similar to Vancouver's Skytrain. In London that would be the tube, in Paris, the Metro. Do your research and ask the ticket sellers (inside the station) if there are any discounts if you are a student, under 25, or a traveler. Sometimes they have day passes or it may be cheaper to buy in bulk. Pay attention to signs or posters within the station. When I was in Lyon with my best friend, they had a big sign on the wall describing the ticket options and then you bought the tickets from a machine. Luckily we noticed that there was an additional option listed on the computer screen which offered a day pass for cheap. It saved us at least 10 euros each and a lot less walking. You should also ask the ticket seller for a map of the routes. This should be free if the map is available.
Buses are harder to figure out but provide a great way to see the city if you have the time and patience. Some cities, like London and Rome, have tour routes that go along major attractions. You will probably have to buy the bus guide though as most will not offer it for free.
Outside of a city, it is pretty much the same options with the addition of planes. How you decide between the three depends on what your priorities are and what your travel plans are. For ease of analysis, I have listed the pros and cons.
- on time and dependable (if not on strike)
- good views (especially on scenic routes)
- more time options available (such as night train which saves you a night at a hotel)
- longer travel time
- need to move your own luggage on and off the train as well as finding your own storage area
- shorter actual travel time
- cheaper cost
- not very time efficient (need to check in, go through customs, waiting at the gate, delays)
- fewer time options
*Train is the better option over bus 99% of the time unless the bus route is more scenic, you do not care that it takes a longer time and it is much cheaper or just that the train does not go to your destination.
Eurail passes can be quite useful but it goes back to what your itinerary is like. There are many different types of passes, so spend time on the website and buy them before you leave. It is much better to have it with you before you leave.