We recommend using the vast metro network in Paris. It’s relatively cheap, quite fast and very flexible. Paris has 14 metro routes in total, and they are all color-coded. Read more about the Paris metro.
When you’re not really into traveling by metro, you should try city buses. They’re not as flexible, but they’re also quite cheap and they can get you to more specific places, which is convenient if you’re not just looking to visit the main tourist attractions. Read more about Paris buses.
For a little more luxury and privacy it’s always possible to take a taxi. Taxi prices vary, but are much higher than other public transportation methods. Not very cost-effective, but a great way to get back to your hotel after a long day/night of walking! Read more about Paris taxis.