We are disembarking from a cruise in Monaco and want to travel to Barcelona, Spain, by train. Is that doable?
Michael, Yes, that is "doable" but it will be a long ride, between 9.5 and about 18 hours, depending on which train you connect with. What day does your cruise arrive in Monaco? A better (and faster) option would be to travel by train to Nice and then use a budget flight to Barcelona. For example, EasyJet has flights on that route, although they don't operate every day (flight time about 1.25H). You could check Vueling or other airlines as well. Happy travels!
Some more details to add to Ken's excellent summary: To look at train schedules, follow Rick's tutorial about using the German Rail site: http://www.ricksteves.com/plan/tips/db_tips.htm. Note that this will not give you prices for your route, but will give schedules and connections. To look for flights, use http://www.skyscanner.com. The airports you want are Nice (close to Monaco, with a direct bus connection) and Barcelona. Be careful of flights to Girona Airport and calling it "Barcelona"; Girona is a lovely town, but it's about 90 minutes from Barcelona.