Public transportation in Paris and suburbs is excellent. There is always one way or another to reach your destination. The prices are manageble and for most places the departures are often and regular. Within Paris itself it's the metro that covers, while the RER is the train to and from the suburbs. The system is easy and practical, but takes a bit to get used to.
On every metro-station you can find maps over the system. There are 14 different metro-lines where some has their destination outside Paris proper in zone two. All departures are listed according to their destination. Unlike London, where you have to know in what direction you take the train, you in Paris have to know the destination of the line.
To use the metro you need to use the socalled "t+" tickets. They're valid for both metro, bus and RER in Paris. As long as you are within the metro, you can change between lines as you wish. You need to carry the ticket during the entire trip and can't throw it away before you leave the metroe. There are stations where you have to pass the ticket through the machines to get out.
There are different discounts for metro and RER, but the most practical for visitors is to buy a "Carnet de 10 tickets", which is ten tickets with a small discount. One "carnet" costs 11,10€, where a single t+ ticket costs 1,50€. Children from 4 to 9 years are "tarif réduit" which is half price. Children under 4 are free.
As a tourist you can buy a "Paris Visite" ticket, which can be used unlimited during the period it's bought for. It can be bought for zones 1-3 or for zones 1-6, which covers the entire RER/metro system. They're valid from 1 day to 5 days. Prices can be found at the homepage for RATP.
There is one thing you need to keep track of, and that is the strikes. To strike is a people's sport in France, and it's almost always the transport sector which is immobilized. If there's a strike while you're visiting, then prepare for a public transportation which is chaotic, disrupted, and non-functioning. Expect sore feet.