Just walk in the station and buy a ticket as usual? Or is there anything else I should know?
Just answered a similar question over here. You're basically right, you buy a ticket or a pack of ten, they're paper with little magnetic strips on the back. You validate it (stick it in the yellow reader), then hang on until you're done your journey - sometimes inspectors will ask to see it. Other parts of France are pretty similar, and the buses are the same. Enjoy your trip!
There are two cases to consider : either you travel on city transit systems or the national rail network.
City transit systems
Most cities in France work the same way.
Buy a ticket before you go. It is a flat fare in most cases. Getting the tickets in bulk (booklet of 10 tickets in Paris, 10-trip ticket in other cities such as Bordeaux) gets you a discount on the price of the single trip. All-you-can-ride passes for one day, one week, a few days... are available depending on the city.
All metro and tram (light rail) stations have ticket vending machines, as well as some important bus stops.
If you take the bus, it is not common to buy at the driver; that's more in case on "emergency"; you'll often need near-to-exact change, pay a more expensive price and not benefit of free transfers, all if the driver has not sold out all his ticket stock. If out of tickets and beginning the trip at a secondary bus stop, look for "dépositaires" (newspaper stands, book shops, tobacco shops, cafés...) which are entitled resellers of tickets for the city transit system; you may find the transit operator logo hanging over the shop entrance. For instance, in Paris, this is a giant metro ticket.
When you board a bus or a tram, there is a validator near the door in which you have to time stamp your ticket. In metro (undergound), this is done while passing fare gates.
Some Metro networks (Rennes and Lille) use a honor system; there is no gate, but you have to use the validator before walking beyond the line which is the paid area limit.
Hold on your ticket until your trip is over; there are random checks in the paid area or when exiting busses. The first validation begins the travel period (usually 1h30) in which you can transfer for free to other lines in the system. No ticket... well, it's an immediate fine of an average €40!
The Parisian case
In Paris, the standard T ticket is valid on all Metro lines and RER in zone 1.
To reach outside these limits, you have to buy the exact station-to-station ticket you need, or use a pass that includes all the zones you need to travel on. There is no fare adjustment on exit; if you travel further than allowed by your ticket, you may be fined in case of random inspection.
Most bus and tram lines in Paris and close suburbs use T tickets too, whatever the zone.
One ticket is either valid for travelling on Metro + RER, OR surface modes (bus + tram); there is no transfer between Metro and bus with a single-ride ticket.
Long distance trains are operated by SNCF. High speed trains (TGV) have reserved seats only, as well as a few non-high speed long distance lines and overnight sleeper trains. In such cases, pricing is driven by yield management and goes up as the train fills up. Tickets for reserved trains are valid on the designated train only.
Other, non-reserved trains (Intercités and TER) have fixed pricing. Discount card holders have to take care of the departing time; the discount may change if it is blue (non-rush) or white (rush) period. Tickets may be valid on any train on a designed period even if there is a specific train time on it; you may check that if your ticket says "Billet utilisable du ... au " with the mention "Départ en blanc" (rush) or "Départ en bleu" (non-rush). To know which are the "blue" and "white" times, check at the station near the ticket windows.
Tickets can be bought using a credit card at the yellow machines, or directly at the window. It is also possible to book by phone, online on voyages-sncf.com, reserve or prepay on the website and have the ticket printed at the station using the "numéro de dossier" 6-letter reference. If you just prereserve this way, be cautious that your reservation may expire. A recent system is the "e-billet" that allows you to print your ticket at home.
Once you get your ticket, you have to time-stamp ("composter" in French) it at the small yellow machines in front of the platform access before you board. Then just enter the train and find your seat if it is reserved.
You do not check your luggage like at the airport; board the train with it and deposit the big pieces in the big racks near the entrance. If there is few room available, do not hesitate to play Tetris(R) with the other bags to get a space to fit yours. Smaller items fit in the overhead racks.
In case you forgot to time-stamp your ticket or you do not have any, signal it promptly by yourself to the conductor as he does a first walk-up of the train shortly after departure, before ticket checks have started. I do not advise to purchase on board although it is possible; you will pay the most expensive fare and a surcharge. There is no surcharge if you board from a small unstaffed station.
Note about iDTGV and Ouigo : these are the rail equivalent of low-cost airlines (Southwest, Ryanair, easyJet), also operated by SNCF. Tickets are exclusively sold online. Ouigo can have nice fares but hefty luggage restrictions.
Commuter / regional trains
If your destination is in Paris suburbs, you'll rely on the RER or the Transilien. These work with the same kind of tickets as Paris Metro. Since you are travelling outside Paris, the fare depends on the distance; you need to buy a ticket with the names of your departure and arrival stations. Any station in Paris is "Paris" or "Zone urbaine", valid from or to anywhere in the city. All the network is single-class.
In other regions than Ile-de-France, the regional rail is called TER for "Train Express Régional". Check the schedules since these run less often than Transilien; tickets should be bought and stamped like any long-distance rail tickets. Some regions have first class aboard these trains.
Long-distance bus is not really developed in France. Most lines are international, operated by Eurolines, iDBUS, Megabus and others. In some cases, you can do domestic trips.