You should know that there are (approximately) 3 types of trains that will take you around and in and out of Paris. They are:
- The Métro: The métro is what New Yorkers would know as the subway or Londoners would know as the Tube. It runs (mostly) underground within Paris, with trains running every few minutes from roughly 6 a.m. to midnight. It is run by the RATP, Régie Autonome des Transports Parisiens (Paris Public Transit Company, which also runs the buses and tramways within Paris). If you have a transit pass such as a Navigo you can use it on pretty much any métro train, bus, or tramway and also on the funicular that takes you up the Butte de Montmartre to Sacre-Coeur.
- The RER: The RER is a small train that runs within Paris and out to the Paris suburbs. The letters stand for Réseau Express Régionale, i.e. Regional Express Network. For certain destinations within Paris it is easier to take the RER than the métro. If you go outside the city center to a place like Euro Disney or Charles de Gaulle Airport, you will take the RER. It is run jointly by the RATP and the SNCF, Societé Nationale des Chemins de fer Français (French National Railway Company, which also runs the grands lignes). The RER, like the métro, runs from roughly 6 a.m. to midnight. Your Navigo will take you only so far on the RER, so be careful. If you are going to Charles de Gaulle, for example, you will have to pay extra because it's a longer trip.
- The grands lignes ("major lines"): Run by the SNCF, these are proper trains that will take you from the main train stations in Paris to other cities in France and beyond. For this type of train you have to buy a ticket and, in many cases, get a reserved seat. They leave from one of the seven main stations depending on the direction/region they serve. The hours are more limited because the journeys are longer. The SNCF runs several different types of trains, including the well-known TGV high-speed train.
If you know the differences among trains you can figure out how to get where you need to go and how to pay for it. The métro and RER are very easy and fast once you learn to use them. The major lines are a great way to see some countryside en route to your destination.