The best way to travel in Paris is going by public means of transport, especially the underground, whose 11 lines take you everywhere actually (there are 273 stations in all). Of course the underground takes you to all the touristic places, the most interesting ones and so it takes little time to move from a point of interest to another. A single ticket costs 1,30 € while using a carnet with 10 tickets, which costs 10 €, you can economize.
People staying more than few days in Paris or intentioned to frequently travel by underground should buy a “Paris visite” card that lets you travel in Paris without worrying about buying tickets. Underground Map Stops and points of interest Official site (in French)
Bus
Don’t forget the bus service: you will visit the city not “place by place” but enjoying those many views you can’t catch otherwise travelling by underground. Bus Map
Taxi
Another possible chance to travel is going by taxi, not very cheap of course, but fit for demanding customers.
Car-hiring
Since it is impossible (or expensive) to park, using a private care is not recommended. Anyway there are the greatest car-hiring companies in Paris: prices vary according to the car and to the hiring period.
Paris Visite
To visit Paris economizing and not worrying about the underground tickets or the access of some of the main places to visit there’s Paris Visite card. Paris Visite