The suburban trains are run by the nationalized French railroad system - SNCF. These trains leave from all of the train stations (which are also served by the Metro, bus, and RER.)
Not only can you reach the rest of France and Europe from these stations, but the suburbs too.
You will need to buy tickets based on your destination.
Grande Lignes: If you are headed further than the suburbs, say to Brittany or anywhere in France or Europe, then you will need to go to the ticket counter with the sign that says Grande Lignes. There is usually someone there who can speak English if your French is rusty.
Banlieues (suburbs): There are Banlieues ticket counters (don't wait in the Grande Lignes line) as well as automated machines. If your French is rusty, than I suggest the machines since you can click on the little British flag for and English translation. They are touch screen machines which can take cash, coins, and credit cards. You type in the suburb to where you are headed, ie. Versailles, and then tell it what kind of ticket - one way/round trip. Then it prints it out for you. The machines will give you town choices as you type in the letters. This is helpful because it can be hard to remember the exact name and spelling.
Note: Even with my good luck with ATM and Credit Cards, I still have spotty success using them with these machines. Try your card first, but always have cash/coins as backup!
FINDING YOUR TRAIN
Once you have your ticket, go to the main platform of the train station. This can be daunting as there are often 20 lines. Look up at the electronic boards at the end of each track to see where the next train is headed and at what time. Ask for help if you need to, even a chic Parisienne will usually be glad to help point you in the correct direction.
VALIDATE (COMPOSTER) YOUR TICKET
At the end of the track, there is a small box in which you slide your ticket and then it clicks (just like the bus). Be sure to do this and then keep your ticket handy. The SNCF are "controlling" for valid travelers quite often now and I do not count these ticket controllers as the friendliest bunch. But they are doing their job so don't think ill of them. Think of the parking ticket and speeding ticket people in the States. Just follow the rules and you'll have nothing to worry about.
Since the trains run often, it would be wise to miss the train about to leave so you can validate your ticket rather than risk breaking the SNCF rules! If your ticket has not been validated, I believe they'll ask for your passport, chew you out and then I'm not sure what happens. But it's sure to "derail" you for a while.