Availability of local train tickets in France

If you plan to depart from the airport train station (Lyon Saint-Exupéry TGV), there are no easy connections to Grenoble. This station is served by high-speed trains on a north/south axis and Grenoble is on the east.

You can take the Rhonexpress light rail (a bit expensive) to arrive at Lyon Part-Dieu, the city's main station, 30 minutes later. Rhonexpress tickets are bought at the machines.

From Lyon Part-Dieu, there are trains to Grenoble. In France, there is a rule: TGV have mandatory reservations; day Intercités and TER (regional) are non-reserved. You can use the regional ticket machine directly at this station.

If you do this leg on a TGV, however, you'd better reserve in advance to get better fares since yield management applies on trains with mandatory reservations. Then you can pay online by credit card, note the 6-letter "numéro de dossier" reference, show up at the station and use a yellow vending machine to print your ticket.

I would not take the train from Lyon Airport to Grenoble. It is not very convenient. However, there is a bus connection between the two cities, operated by Faure Vercors. The buses run hourly between 5h30 and 22h30. The price for a return ticket is 33 EUR and it journey is a roughly 1 hour.

You can safely buy a ticket in advance. If your plane is delayed you can catch a later bus. This is stipulated in their general terms available on the site (in French).

If you do want to take the train go to www.voyages-sncf.com to buy your ticket. Some tickets are refundable or flexible others are not. You will see that during the booking process.

Update

If you decide to go by train, be careful. There is a lot of noise in the answers here.

There is a train station next to the airport. This station is called Lyon Saint-Exupéry TGV. From there you can get direct TGVs to Grenoble. They are not very frequent though and hence not very practical. This is a 1 hour ride. If you want to take a TGV it makes sense to book a ticket in advance. If you buy a flexible ticket you can change it or ask for a refund if ever you miss your train.

There is another station called Lyon Part-Dieu. This station is in the center of Lyon. To get there by public transport from the airport, take the Rhônepexpress tram, as actually indicated by @Davlink. If you buy the tickets online, you can save some money. Have a look at their website and you will see. From the Lyon Part-Dieu station you have to take a regional train (TER) to Grenoble. They are running frequently, one or two per hour. It is not possible to make a reservation on these trains. Buy a ticket at the station and hop on the train. You can of course buy an online ticket beforehand. It just avoids you to queue at the station. Eventually, this option, Tram+TER, takes twice as long as the bus and is twice as expensive.

In France regional (local) local trains are non reserved. Outside Paris these trains are called "TER" trains. For these trains advance booking is not needed, as prices are the same weither bought on the spot, or in advance. So you don't need to "book" this, just buy it at the station. A ticket for TER trains allows you to take any train on the route mentioned on the ticket, within the period of validity which is also mentioned on the ticket.

It is only for long distance trains, like the TGV high speed trains, and the "Intercités" that you need to reserve a seat in advance, and where prices can be different based on when you travel and when you book.

Contact the airline company and ask if they participate in a system similar to Rail&Fly offered in Germany by Deutsche Bahn. This system allows you to buy tickets for high speed trains to / from any destination in Germany, following airplane arrival / preceding airplane departure. As delays are possible, these train tickets, naturally, are not bound to a specific time. Depending on distance, these tickets can be quite a bargain.

A quick web search shows up a system in France called tgvair. The TGV in tgvair apparently refers to France's high speed rail service.

On my website loco2.com we sell local train tickets within France. You can choose print-at-home as a delivery option and receive the tickets by email to print off before travel. Here is an example search for Lyon-Grenoble departing in May:

http://loco2.com/journey/lyon-grenoble-5e4ibx

As you can see in the search results table, the journey from Lyon to Grenoble takes just under 90 minutes. The tickets available via the above link have "fully flexible" fare conditions, and so you can use them on any train on the date specified, but you will only have seat reservations for the train you choose.

For the Lyon-Grenoble journey above the prices do not become more expensive, so you can book late without paying more. For other journeys where there are non-flexible/non-refundable tickets available, you can usually save money by booking earlier. The disadvantage of this is that you are then restricted to travelling on one particular train, so you should upgrade to more flexible tickets if required.

There are lots of other websites that sell the same tickets as Loco2, including voyages-sncf.com and TGV Europe, both of which are owned and operated by the French national rail operator, SNCF. Prices on Loco2 are in UK pounds, but apart from that are the same price as booking direct with SNCF for most journeys.

You can of course purchase tickets on the day of travel as well. This will usually be more expensive than booking in advance, and you will need to leave time to purchase the tickets before your train departs.