If you are like me you will walk. This is for two reasons. One I like walking because it is the best exercise you can do and in a city like Paris there is plenty to see when traveling on foot. The other reason is because I am mentally lazy and for me it is easier to walk two hours to get somewhere then it is to take two minutes to learn which bus or metro to take that will get me there in ten minutes. Luckily there are plenty of people not like me that keep the buses and metro in Paris in business.
The Metro: The Paris metro is one of the oldest and one of the best systems in the world, right up there with London and New York. There are around 300 stations connected by nearly 300 kilometers of track. You can get within a couple blocks of anywhere you want to go. The metro runs from 5am to 12:30am and for the price of a ticket you can ride around all day long if you like. (as long as you don't leave the system). Tickets can be bought at the ticket booth in the station one at a time, by ten or by 1-day, 2-day, 3-day, 5-day, Le Paris Viste tickets for tourists. There are also weekly and monthly tickets called the Carte Orange. It's a travel pass good for unlimited travel on the paris metro and bus network. You need a passport photo to buy this, but if you use the metro a lot it's worth it. (more that 6-8 times a day). When you use your tickets stick it in the turnstyle slot and then take it when it is returned to you and keep it with you during your trip. Occasionally the check and getting caught without one can be embarrassing as well as expensive. You can get metro maps at the stations and they are posted all over the system. You can also find them in most of the guidebooks though some are so small you will need a magnifying glass. If you can master the Paris metro system you will travel around the city in confidence and never want to leave. The maps are color-coded so all you have to do is find the station you want to go to and find the line that goes there and see what the final destination for that train is. Then follow the signs for that destination and when the train comes get on and just remember to get off at your stop. Here's a Paris Metro Map you can use to familiarize yourself with the system.
The RER Train: This is a sort of suburban line that goes further outside the city though it has several stops in central Paris and in some cases may be more convenient. You can use your metro ticket on these too, but only in the central part of the city. If you are taking them out of the city you need a separate RER ticket. There are four lines and of these you will probably be most likely to use Line C to go to Orly Airport, Line B to go to Charles De Gaulle or Line A to go to Disneyland. Here is a Paris RER map that you should find useful.
Buses: The bus system is also exceptional and unlike the metro which is fast but sort of redundant (since after awhile all tunnels look the same), traveling above ground is not only more entertaining but a good way to familiarize yourself with the city. Metro tickets can be used on the buses and can be bought on the bus as well as in the metro stations. There is a machine on the bus that stamps your tickets and then hang on to them since there are guys who come and check them every once in awhile. To transfer you need another ticket. Le Paris Viste and Carte Orange tickets need to be shown to the driver. There are bus maps available at the metro stations and posted in the bus shelters. Most buses run from 6:30am to 8:30 pm but there are a few buses which run until 12:30am.
Taxis: There are almost 15,000 Taxis in Paris and finding one is usually not a problem. There are taxi stands all over the city and you van also hail them in the street if the taxi light is bright. If it is dim that means it is occupied. Taxis are relatively inexpensive and the easiest way to get home after a day or night of walking around. You can usually have your hotel concierge call a taxi if you don't want to try your luck on the streets. Taxi driver are generally friendly and like New York come in a large variety of nationalities.
Boat: The Batobus runs up and down the seine with six stops between the Eiffel Tower and the Quau de l'Hotel de Ville across from Ile de la Cite. The boat runs from mid-April to mid-October
Driving and Biking: People driving to Paris are advised to leave their cars somewhere and forget about them. You won't need a car in the city and even if you do, driving can be a terror to the uninitiated. Parking is even worse. Car rentals are usually for a minimum of three days so save your day trips outside Paris for one long stretch and turn them into overnights if you feel you need to use a car. Otherwise take the trains or do a tour. Bikes can be rented and there is a map of the bike routes through the city available at tourist offices and bike shops. If you are planning to cycle the countryside outsoide of the city it it best to rent a bike at your destination rather then renting one in the city and riding out. There are bikes availabe at a number of train stations. For more information on cycling in Paris contact the Federation of Cyclotourisme at info@ffct.org or visit their website at www.ffct.org