Whilst acknowledging that Battersea has already purchased the required tickets, I will just add the following information, as it may be of use to others.
I travelled from Berlin to Prague the week before last using a train-specific advance purchase ticket bought from the DB site. It cost about £31.
I returned north last Monday, but purchased that ticket from the CD website, as the price was around £24 for the same type of ticket. Unfortunately, the CD site can only sell tickets originating from the Czech Republic.
Tickets from both sites were purchased using a standard British Visa debit card - which was required to be shown along with the DB home-printed ticket. My passport was the required ID for the CD ticket.
Trains run every couple of hours and the journey takes about four and three quarter hours, with plenty of slack. The journey between Berlin and Dresden is quite dull and feels like a stagger, but south of Dresden the line is lovely and feels quicker. Try to sit on the left hand side leaving Berlin for the best views of the river valley south of Dresden.
The trains are hauled by DB Class 101 loco's between Berlin and Dresden and CD Class 371 loco's south thereof. Air-conditioned CD second class compartments on the route tend to have six wide reclining seats, curtains, adjustable temperature, lighting and PA volume, along with power sockets, which are hidden behind the curtains. However, I think the 08:45 from Berlin uses Austrian stock and cannot advise on the features found on the train.