RER (Réseau Express Régional) is the train system which connects the suburbs with Paris. It is fast and very effective. There are 258 stations and 587 km tracks. In Paris proper there are 33 stations and they have direct connection to the metro. Line A has up to 55.000 passengers per hour in each direction, which is the highest in the world outside of Japan.
The system is built on zones as we know it from Denmark. Paris itself is zone 1 and then you'll find the zones in rings around Paris. There are 6 zones. Disneyland is in zone 5 on the line A, while the airport Charles de Gaulle is on line B in zone 6, and the airport Orly is at the other end of line B in zone 3.
Several of the RER stations are also SNCF stations, which is the national railway. They cover the less dense areas and other towns around Paris' suburbs. Normally you just need one ticket no matter which railway you take.
There are machines on all stations, also the metro, where you can buy tickets for the RER. You purchase the tickets directly from station to station and you don't need to think about the number of zones. All credit cards with chip can be used or you can pay with coins. The machines are also in English and other languages, so you don't need to fight the French phrases.
A ticket is valid between the two zones it's bought for and has to be kept until you leave the final destination. All stations in zone1/Paris are just named Paris and you can change directly to the metro without buying a new ticket. You can also get of the train a station or two before your destination and still get through the control machines. The problems only arise if you get of the train too late. Luckily it's easy to get to the other track and catch a train heading back again.
If you have to travel several times between two stations, or in a group, it's always worthwhile to buy a "carnet" holding ten tickets. There's a significant discount.
http://www.ratp.fr/ - Here you'll find travel plans between all stations in Île-de-France, as well as maps, schedules and prices.