Book on sncf-connect.com, the operator's own site, where the same route is sold under TGV INOUI, OUIGO, Intercités, and TER brands depending on the train; direct TGVs are the ones to look for, since the others add a connection. Fares open about three months ahead and the cheapest seats go first. First departure from Paris is around 6:40 a.m. and the last in the evening, so a morning TGV puts you at the Grotto by mid-afternoon, in time for the 5:00 p.m. Eucharistic procession and the 9:00 p.m. torchlight procession.
The night train is the pilgrim's classic. It runs from Paris Austerlitz with couchettes and arrives in Lourdes early enough, as the local tourist office puts it, to make the most of your first day; check the days of operation because it does not run every night of the year.
From the station the Sanctuary is a walk of roughly 20 to 25 minutes downhill through the town, or a short ride on the city bus; the Sanctuary says only that urban buses connect the station with the Sanctuary quarter and does not publish the distance. Taxis wait outside. The station has a ticket office, machines, luggage lockers nearby, and assistance for passengers with reduced mobility, which matters for pilgrims traveling with a wheelchair. If you arrive by air instead, the existing page on getting to Lourdes from the airport covers Tarbes-Lourdes-Pyrénées, about fifteen minutes from the Sanctuary.