The metro is the ideal way to get around Paris fast and easily. There are 16 lines (including 2 "bis") traversing the city. At any given Metro station each Metro line will have 2 platforms, one for each direction.
Upon descending into a Metro station line platform, find a Metro map located on the platform wall. Find the current station you're at and then find the station you're traveling to. Once you find the destination station on the map, follow the Metro line to its end, the terminus, which will be the direction name you're after for this Metro line. By keeping the terminus stations in mind when switching Metro lines, you'll know which lines and in which directions you must travel to get to your destination.
The Ile de France region is divided into 5 concentric zones. The Paris metropolitan area fits into zones 1-5. CDG airport is in zone 5, Orly and Versailles in Zone 4. The city of Paris, within the Périphérique, is Zone 1. A RER Ile-de-France zone map can be found online.
Buses are also a great option as they allow you to see and enjoy the city while moving around. There are so many buses in Paris, you can go almost everywhere by bus. The only issue is to find where they stop! Bus stops are trickier to find than metro stations. Tickets are the same as the ones you use in the metro. A "t+" ticket allows transfers among buses for up to 90 minutes from the first trip. However, if you buy a ticket on board the bus, there are no transfers. Also, there are no transfers between bus and metro.
Keep in mind that the Parisian metro stops between 12.30 and 1 am, and buses usually stop between 9 and 10 pm, with reduced service continuing with night buses and Noctilien buses. Always look for your night bus itinerary before using it.
The RER is also a good way to get from one point to another very fast. The lines are fewer though, so are the stops. It’s mainly used to travel to nearby suburbs, but can be convenient to cross the city in minutes. Although the Eiffel Tower has a metro station at Bir-Hakeim on Line 6, the closest access is through a RER stop (Champ de Mars - Tour Eiffel). Tickets are the same as metro tickets, but you must be careful if you go outside of Zone 1 around the city, which requires a billet Ile-de-France rather than a normal Ticket t.
Commuter rail (Trains de banlieue in French)
If you need to go in suburbs that are located a bit further from Paris, or just not reachable in RER, you may need to use SNCF commuter trains. All of the 6 Paris train stations have trains for the suburbs. (Gare Saint Lazare: western and south-western suburbs; gare de l’Est: eastern suburbs, gare du Nord: northern suburbs, gare de Lyon: south-eastern suburbs, gare Montparnasse: south-western suburbs, gare d’Austerlitz: southern suburbs).
Some TER trains that serve the cities outside Île de France overlap with commuter trains (e.g. those to Vernon for Giverny, Fontainebleau, or Chartres).
A fun and original way to get about in Paris is the boat. The Batobus is a unique line with 8 stops along the Seine. Batobus stops at every relevant monument in the city (Eiffel Tower, Orsay Museum, Louvres, Notre Dame…).
Trains (Mainline - Grandes Lignes in French)
There are 6 train stations in Paris: gare Saint Lazare, gare du Nord, gare de l’Est, gare de Lyon, gare d’Austerlitz and gare Montparnasse. Each of them serve a different part of France, and some of them also serve other countries. There are RER or metro services to access all of them.
Gare Saint Lazare is located in the Grands Magasins area, near the Opera Garnier, in the 8th arrondissement. Its trains serve western and south-western suburbs of Paris and Normandy.
Gare du Nord is located in the North of Paris, in the 10th arrondissement. In addition to all the northern cities of France, it serves London (Eurostar), Brussels, Cologne and Amsterdam (Thalys), Berlin…
Gare de l’Est is right next door to gare du Nord, in the 10th arrondissement. Its trains mainly serve eastern suburbs of Paris, and cities in the east of France. But there also are some international connections for Luxembourg, Germany and Central Europe (Orient Express).
Gare de Lyon is located in the east of Paris, in the 12th arrondissement. It covers the south-eastern suburbs of Paris as well as Lyon, Burgundy, Franche-Comté, all the south-east of France (TGV Méditerranée), but also Switzerland and Italy.
Gare d’Austerlitz is located in the south-east of Paris, in the 13th arrondissement. It covers the center of France. You can also find old night trains for Portugal and Spain there.
Gare Montparnasse is located in the 15th arrondissement, in the south west of Paris. It mainly covers western and south-western suburbs of Paris, but also all the west and south-west of France by TGV.
To find your way to the station, check the RATP website (metro, bus, RER).
The almost free bicycle system in Paris, called VELIB (a contraction of Velo = Bike, and Libre = Free), is an excellent way to get around Paris, particularly for short trips.
The terminals provides a selection of languages that makes it easy for non-French speakers to use Velib.