Lyon, France to Cinque Terre

I'm not sure where you are looking for trains, but the Bahn website is usually the best place to look for schedules http://reiseauskunft.bahn.de/bin/query.exe/en Putting in tomorrow's date, I see trains taking about 10 hours and involving 2-4 changes. You cannot get prices or buy tickets on the Bahn site unless the route involves Germany travel. To actually buy these tickets, you'll probably get the best price by buying the portion from Lyon to Turin or Milan on the French rail site ahead of time, and the potion within Italy on the Italian rail site ahead of time. If you need help with this, ask here. Tickets bought on the day of travel will be MUCH more expensive, for both France and Italy. If you're looking on Eurail, stop immediately - this site exists to sell rail passes and marked up tickets, and only shows routes it sells. In general you want to use Bahn's site to find schedules, then the site of the country of origin of your train to book (exceptions exist, of course). Connections between France and Italy are not as good as most American think they will be. Actually, the same is true of some other country pairs, like Spain and Portugal. If your trip is not set yet, you should look at connection options before booking hotels.