Paris Metro & RER
One of the easiest way to travel inside Paris is using the Metro of Paris, and the faster RER ("express regional network"). The Metro was inaugurated in 1900, making it the second oldest on the continent. It is also Europe's most extensive (297 stations on 221.6 km) and busiest metro network, with over 4.5 million passengers per day (50% more than London).
=> Map of the Parisian Metro network.
Bus & other public transports
An alternative to the Metro is the bus, and in some areas the tramway, all managed by the RATP, like the metro.
Since July 2007, the government of Paris has installed hundreds of bicycle stations around the city, providing thousands of bicycles with automated rental 24 hours a day, 7 days a week. The system is easy; buy a daily, weekly or yearly subscription card with your credit card, then rent a bike and return it to any Velib docking station whenever you want. Stations are distant of about 300 meters from each others.
A one-day card cost 1 &euro, while a yearly card is 29 €. The first 30 minutes are free, 1 € for the second half-hour, 2 € for the third half-hour, and 4 € for any additional half-hour. More information on the website of Velib.