Reservations for this train can also be made on the Czech railways website. Enter "From", "To", select 1st class and set the correct no. of passengers. Then, in the overview with connections, click on "I want a reservation only” for the connection you want. The reservations will be delivered via email. They will also be much cheaper than via the Eurail reservation service.

You can find in this post a short manual for Ceske Drahy/Czech Rail reservations  (example is for a Nighttrain but for daytrains it´s even easier )

During the trip, I've noticed that the cheapest and surest way to get seats is to go to the some station in the countrya nd buy them from there. It’s old-fashioned, of course, but it’s worth it if it’s possible.

Thanks all! I went to the Czech Railways site and *I think* I properly reserved seats. We shall soon see!

You finally should get a paper with a QR Code :)