The current train service: you catch a fast train from Sants station in Barcelona to Figueres-Vilafant. From there you have a direct cross-platform connection into a TGV (Train a Grande Vitesse - literally 'high-speed train') which will take you into Paris. This service runs twice a day, with a morning and afternoon departure.
This is how the 'Man in Seat 61' recommends you make reservations - the instructions are from Paris to Barcelona but just reverse the processes.
>>> I recommend splitting the booking into London-Paris, Paris-Figueres and Figueres-Barcelona (or Figueres-Madrid etc.), booking each train at the relevant operator's website. This way, you'll get the cheapest price for each train with no booking fees, you'll get a full choice of seating options including upper or lower deck for the TGV, and you'll usually get a print-at-home ticket for each train, so it then doesn't matter where you live as nothing needs to be posted. Obviously, do a dry run on each site first to confirm availability & prices.
Step 1, go to www.voyages-sncf.com and book from Paris to Figueres Vilafant, looking for the direct afternoon TGV train, and buy your tickets. You'll usually get a print-at-home ticket, or in some cases ticket collection in Paris.
Step 2, now go to www.renfe.com, click 'welcome' for English, then click 'Purchase', now enquire for Figures Vilafant to Barcelona, Zaragoza or Madrid. Identify the train that connects with the TGV you've just booked and buy the ticket.
Note that you may see what appears to be two trains with exactly the same times, one an AVE and one an Avant. These are in fact one and the same AVE train on which Renfe sell a few cheaper Avant fares for shorter journeys. Just select the cheapest fare in the class you want on whichever train. A cheap Promo or Promo+ fare is the one to go for, if available. You'll be offered a self-print ticket, and the job's a good 'un.
Renfe.com sometimes struggles with overseas credit cards, and it has a few quirky translations, so if you have any problem, simply book the train from Figueres Vilafant to Barcelona, Zaragoza or Madrid train using www.petrabax.com/renfe instead. This is a US agency which links to Renfe's ticketing system, with their cheap Promo fares available. Naturally, they charge a small mark-up, but it's in plain English with no payment problems. You can also try www.raileurope-world.com, who now also have a link to Renfe. <<<
There's more information here about the journey, including what the trains are like - simply ignore the bits about London and Eurostar. It's entirely up to you whether you want to pay the extra to go first class. Note that you are responsible for your own luggage, and there is storage space for it inside the carriages - there is no 'checked baggage' like in Amtrak, the concept simply doesn't exist on European trains.